Can my landlord make me pay a pet fee and deposit on a dog I'm babysitting?

i've been babysitting my mother-in-laws 3lb yorkie and i received a letter from my apt saying i have to pay a pet fee and deposit on her. my lease is up in march and we are moving, that is only a month and 1/2 away. can they make me pay this pet fee and deposit? The letter states "We are now requiring a... show more i've been babysitting my mother-in-laws 3lb yorkie and i received a letter from my apt saying i have to pay a pet fee and deposit on her. my lease is up in march and we are moving, that is only a month and 1/2 away. can they make me pay this pet fee and deposit? The letter states "We are now requiring a pet addendum be placed in order to continue keeping this dog in your home." Once the dog goes back home, can they still make me pay this? I had already told one of the girls in the office that the dog does not belong to me.
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