Mirror Image still works while grappled
The question is inferring to the ability of the grappler to make an attack on a grappled subject who has casted Mirror Image after having been grappled.
The full description sighted at the end of Mirror Image reads as:
A creature is unaffected by this spell if it can’t see, if it relies on senses other than sight, such as blindsight, or if it can perceive illusions as false, as with truesight.
(page 260 PHB)
Once we have the full description we can see that the spell is referencing a special ability and a catogory that D&D 5e refers to as senses. Further research will lead towards both the Dungeon Masters Guide (page 279 DMG) and the Monster Manual.
STEP 19. SENSES
A monster might have one or more of the following special senses, which are described in the Monster Manual: blindsight, darkvision, tremorsense, and truesight. Whether the monster has special senses or not has no bearing on its challenge rating.
On pages 8-9 of the MM in another section titled Senses it goes on describe the senses in detail. It is of note that DMG is refering to the creation of monsters and the MM to describing monster abilities, but in D&D monsters infer to the creation of enemy NPCs that can also include humans, dwarves, elves and such. Therefore these are the senses that the spell is pointing at since it includes actual examples of what it refers to as senses. If the grappler has none of these "senses" then it should be understood that the spell comes into effect, even after the caster has been grappled.
A popular argument also seems to point at "touch" as being a sense, and for the sake of argument let's run through it. Page 204 of the PHB describes illusion spells as follows:
Illusion spells deceive the senses or minds of others. They cause people to see things that are not there, to miss things that are there, to hear phantom noises, or to remember things that never happened. Some illusions create phantom images that any creature can see, but the most insidious illusions plant an image directly in the mind of a creature.
This is very important since this strengthens the case about special "senses". Touch is interpreted though the brain aka the mind. Therefore if you do not posses blindsight for example, you cannot perceive what you touch as real.
I still would allow the grapple to continue, there is no escaping that. But once the grappler takes an attack action he is subject to the conditions of Mirror Image.
If the DM still doesn't see it that way, and house rules that touch effects the casting of the spell, minimum I would recommend the grappler at least spend as action doing a Wisdom Perception check. Even a cantrip like Minor Illusion has a condition like that for physical interaction with an illusion.
If a creature uses its action to examine the sound or image, the creature can determine that it is an illusion with a successful Intelligence (Investigation) check against your spell save DC. If a creature discerns the illusion for what it is, the illusion becomes faint to the creature.
(page 260 PHB)