TOKI NO SHUGOMONO

Toki no Shugomono summary:

A girl named Miu stumbles upon a mysterious pawnshop where the only item for trade is time itself! Everyone always searches for extra time, but are they willing to exchange something that is more valuable and irreplaceable — their most precious memories? These memories could be wiped out forever if the borrowed time is not returned. Tokiya, the shop owner, recruits Miu to work part time as a "Time Go-Between." Her new boss is sweet, but he has his own motives regarding the time he trades. And Miu must always remember the most important rule: Never speak of the shop to anyone.