WoT characters love torturing themselves with their bad memories. See Rand keeping that Seanchan spear as a scepter to remind him not to forget them (and no, he didn't just keep it as a reminder of igloo-loving with Avi xD), Lan forcing himself to look at his Malkieri ring every day to remind him of his oath against the Shadow, Moiraine keeping that stupid little ink bead to remind her to break rules, Amyrlin Siuan obsessively hoarding unimportant documents in secret before she's deposed, Nynaeve's scars on her palms after her Accepted test...
Besides, that bracelet can be seen as a trophy of the time she beat
the Lanfear.

Just wiggle the bracelet in someone's face when they start doubting your awesomeness (not that Moiraine would ever be so unsubtle, of course

) And she didn't get to keep a trophy from Be'lal.