I am putting my money on a screwed up home life that she is ashamed of (in addition to her already bully filled school life) as the explanation for Anri's behavior. She seems to be devoid of hope past the point of being able to enjoy even small victories. It seemed like she gave up looking for her shoes because she just couldn't deal with trying anymore and getting them back didn't put a dent in her general malaise/despair.

I might also put a side bet on an extra long shot just for the lulz. Maybe she wanted Mikado to spend time with her so she tossed her own shoes. Then midway through looking for them with him she realized she hated herself for being such a shady character and went home dejected, hoping he would give up too (retarded I know, but this is for the lulz). Then when Mikado showed up at her house having found the shoes, likely having worked hard looking for her sake to do so, she felt even more dejected at what she had put him through thus inducing a cold response.