if it were even a chashash of true chametz chassidim wouldn’t eat it on the last day.
If it weren’t a chashash, they would be allowed to eat it even on the first seven. It is a slight chashash, so they don’t eat it on the first seven, which are d’Oraisa, but the eighth day is d’rabbanon.
The teshuvah I linked from R’ Moshe Feinstein makes the point that if there were no legitimacy whatsoever to the minhag, it wouldn’t be binding (he is referring to what the questioner seems to say was a minhag to not eat gebrokts even AFTER Pesach), but if there’s even a very slight chashash (which there is), the minhag is binding.
The relevant quotes:
????? ???? ??? ??? ????? ????? ?? ??? ???? ??? ???? ??? ???? ???? ???? ??? ??? ??? ??? ???? ?? ??? ??????? ??? ????? ??? ????? ???? ??? ???? ????? ??? ????? ????? ???? ??? ??? ?????? ????? ?????? ????? ????? ?????? ???”? ????? ?”? ??”? ??”? ?? ???? ?? ??? ???? ??? ??? ????
and
???? ??? ???? ???? ???? ?? ?? ?? ????? ??? ????? ??? ???? ??? ????? ??? ????? ????, ??? ???? ???? ??? ???? ??? ?? ??? ??? ???? ??? ??????? ????? ???”? ???? ??”? ??? ???? ????? ?????