It's an easy fix. The drain pieces have a gasket that goes bad. A new drain piece that screws into the bottom of the sink is about $4-6 US. You will need a pair or channel lock pliers. Some people use a little plumber's putty around the gasket.
When the lease is up, that's your chance to get rid of the tenant. My state goes to a month-to-month implied agreement after a signed lease expires. 30 days notice is all that is required to begin eviction proceedings...or at least threaten them enough to make the tenant move.
It always pays to be on good terms with tenants. If they feel like you are cheating them, then it's easy for them to destroy your place. All a tenant has to do it "accidentally" break a water line and flood everything. You have a lot more to lose than the tenant, at least financially.