I don't know if there is a formal "rule" about returning letters (lavalier) after a break up, but I do know that in my chapter it was a BIG DEAL to lavalier a girl in the first place. It was considered a pre-engagement type of thing, and it was looked down upon for guys to lavalier a girl they had dated for less than 1-2 years.
If a Brother and his lavaliered girlfriend broke up, it was SHAMEFUL for that Brother...like he disrespected the Fraternity by bestowing the letters on a woman that was not up to Dream Girl standards.
So your ex may be ashamed and embarrassed about giving you the letters and then you guys breaking up. I would suggest dropping the lavalier off at his place when you know he won't be there...give it back to him discretely and without his knowledge if necessary.
I'm sorry things didn't work out.