Tenants not wanting to pay pet fees

We have a tenants that does not want to pay for their unauthorized pet. Send them a notice to cure within this week or they may end up with eviction.  

I was debating would it be better to evict after the 1 of May when the rent is due, once I deduct the pet fee from their payment. Then send them an eviction for the rent being short after deduction from the pet fee. Will this consider partial payment that I am holding onto after deducting for pet fee? I was not sure if I need to return the remaining and ask for the full rent in one payment. 

TIA