New tenant requests extra set of keys for non-resident- building security risk?

[Ken D.]

A new tenant asked me if she could have an extra set of keys to give to a friend so that when she leaves town someone can come in her apartment and take care of her cat. On the lease it says, "Resident shall not provide keys to any non-Resident without express permission of the Owner". A part of me feels like this is a building security risk- am I being too strict? This building is a tri-plex and all the tenants are or seem like quality people- the basement is filled with unlocked storage for all the tenants living in the building (a total of 5 tenants). I want to keep my building smart and safe- what should I do? Should I have her pay a deposit on the keys? Or should I just not do it?