It does not
Feeblemind specifically alters your base ability score:
...the creature's Intelligence and Charisma scores become 1.
This spell is a functional to change to your score itself and can only be undone by greater restoration, heal, wish, or making a save after every 30 days. This spell changes your actual ability score from whatever it was previously to 1.
Items such as the Headband of Intellect override your actual score (emphasis mine).
Your Intelligence score is 19 while you wear this headband.
Prior to wearing the Headband, your score was a 1. The text for the Headband is only concerned with what your score currently is (currently 1) and then says"No, when you are using us, your score is 19."
Feeblemind changes your ability score to 1, but wearing the headband overrides that as it would any ability sore and your ability score will be 19. The headband is functionally covering up your intelligence flaws, no matter how you got that intelligence. There is nothing in the spell feeblemind that states the score is unalterable - just that it is turned into a 1 and that certain spells can end the spell effect doing that.
The headband isn't changing your INT from, it's just giving you a 19 while your score is still 1.
Another argument: Instantaneous duration is equivalent to permanence
Big thanks to Carcer for this :)
The change wrought by feeblemind is instantaneous and can't be dispelled. Because of that, it's effect is near permanent with the exceptions provided in the spell for removing it. With that permanent-style change, items that artificially alter scores are still applicable.
I do think this argument is secondary to primary argument that the headband only cares what your score is and states that if it's less than 19 it changes it to 19.
But can an INT 1 attune?
This is the stickier situation, and it's covered in this question - but ultimately, that will be a DM call if they'll allow attunement.