Yeah, there's options here. One of those is actually conceding; your group has misunderstood how that mechanic works.
Option 1: Get Taken Out without taking consequences.
When you have to resolve an attack, you don't have to actually absorb the stress. You just choose between absorbing all of it, or not absorbing all of it and getting taken out. You can even absorb part of the stress, and also choose to get taken out, if it seems narratively appropriate.
This is kind of a good thing because if you were actually obligated to absorb as much stress as possible, every single fight someone's in would be horrifically and permanently character-scarring via extreme consequences, and your story would be filled with characters who need magnitudes more than the usual amount of therapy and trauma counselling.
Fred Hicks himself confirms this is an option in an answer here. He also points out this is a lousy way to avoid harm, since when a character's Taken Out their opponents have complete control over their fate — death and complete and total destruction of the Taken Out character is an option on the table. That's mainly a player's issue though. In this circumstance, what's more relevant is the characters could say these NPCs are concussed out of the mind control (they're free!) and even join the heroes of the story to exact revenge on the person controlling them, or something similar. Anything's on the table.
What this looks like in practice: Decide when the fight is narratively appropriate to end, and let that last punch end it.
Option 2: Concede, because it's not an in-fiction action.
From what I'm reading, you've interpreted concession as an in-fiction action, that the character themselves is saying/gesturing their surrender to other characters, that the fictional characters are fully aware a particular character is voluntarily giving up. This isn't the case.
Like most of the other Fate mechanics, this one takes place above the game, at the table between players. A player says they want a character to concede, the player names the worst parts of the character's fate they want to avoid, and the group then works out how things shake out in the fiction to let that character get taken out of the narrative and avoid that worst stuff.
The Fate Core example of concession demonstrates an example of how this plays out:
Og proves to be too much for Landon to handle in the warehouse conflict, having hit with several devastating attacks in the course of the fight.
Before Amanda’s next turn, Lenny says, “I concede. I don’t want to risk any more consequences.”
[some stuff about fate points]
Amanda says, “So, what are you trying to avoid here?”
Lenny says, “Well, I don’t want to get killed or captured, for starters.”
Amanda chuckles and says, “Fair enough. So, we’ll say that Og knocks you out cold and doesn’t bother to finish you off, because he still has Cynere and Zird to deal with. He may even think you’re dead. I feel like the loss needs some more teeth, though. Hm...”
[more stuff about the players talking and agreeing Og should take Landon's sword.]
In this narrative example, it's not the case that Landon says "Hey! Wow! Og, you're too strong for me. How about you knock me out and take my sword instead." Instead, the players are just talking, Landon's player wants Landon to concede, and they decide the way that should work out is that Og knocks out Landon and might even think he's already killed the guy. Hooray! Og, being a character in the game, is none the wiser about the mechanics that just took place that let Landon live.
This clarification by Leonard Balsera, Fate Core's primary author, further describes the player-facing nature of Conceding.
What this looks like in practice: You decide the mind-controlled NPCs have taken enough punishment and say you're conceding. You say what you'd like to avoid for them (such as: you don't want them dying, or captured, or something) and you and the other players as a group work out how this happens: the mind-controlled characters may get tied up, locked in a room, knocked out, or escape out a window (or get thrown out of one). They never gave up, but meta-game, they've conceded and aren't in the fight any longer.
Just as with being Taken Out, the option of the mind control ending is within the confines of what the players can dictate here. That's unless you chose it as a worst part of the characters' fates to avoid, but you probably won't for two reasons: (1) it's probably not the worst parts of their fate, and (2) you're conceding which means there is bite and you can't have everything your way.
I'll note that a player in control of multiple characters (usually that's the GM) doesn't have to concede for all of them at once. It's on a per-character basis. So you can have Mind Controlled Dude Number One concede, and the other keeps fighting on — and they may also concede or get taken out.
Option 3: Don't use the conflict rules for this to begin with.
Despite the name, physical conflicts don't have to be modelled by the Conflict rules. Reserve the Conflict rules for really pivotal, awesome fights that are super worth zooming in on and engrossing yourself in. If it isn't that, the Conflict is often going to be a pretty boring slog-fest, and my group's learned that one the hard way.
Instead the golden rule suggests you can just model the strife between your characters and the mind-controlled NPCs as a Challenge or just a set of opposed rolls: the goal is to find out who overpowers who and how.
The Avatar: The Last Airbender TV series is an excellent example of physical fights that shouldn't get resolved by Conflicts. Very frequently, the heroes have something they need to do (warn the Earth King about the drilling machine, reach the Fire Nation Palace & find the Fire Lord, reach Avatar Roku's shrine in time for the Solstice) and there are people who are willing to use physical force to stop the heroes from succeeding. However, the heroes are only focused on reaching their goal and using the minimum effort to subdue or evade their enemies: this is prime material for just setting up different enemies as a series of opposition steps in a Challenge, wherein successes get narrated as a whole bunch of people getting beaten up and knocked out, or subdued or evaded.
Avatar also has some really serious fights where things are deeply personal and the only stakes are someone needs to go down: Aang versus Zuko, Aang versus the Fire Lord, So Many People versus Azula, etc. These are gripping, character-defining, plot-defining moments and are worth all the attention and investment of the audience and exploring in depth. Those are the kinds of things you should look to turn into Conflicts.
Challenges and other modelling can still result in consequences or worse if it makes sense: the silver rule provides consequences as a textbook example. If something happens that seems consequence-ey as a result of a challenge or contest or opposed roll, it can be modelled as such. If I physically overcame one of those mind-controlled guys by tossing them out a window, it could make sense to give them a severe consequence (Lots Of Broken Bones) or say they're dead. The Silver Rule says if that seems fictionally appropriate, you can make that the case, and don't let the rules stop you doing that. This means during Contests, Challenges, and other types of modelling, you can still use Consequences — you just don't have to.