Is a text message a written agreement?

In my lease there is a line "No animal shall be permitted in these premises without the consent in writing of Landlord". I have two cats and apparently this was never brought up between my girlfriend and the landlord, or myself for that matter, about the clause or our cats. The landlord 'discovered' the cats and gave us an ultimatum of leaving the property and breaking the lease or getting rid of the cats. I live in NY State and know we have 10 days to remedy the problem. Within those 10 days the landlord texted my girlfriend with an offer for us to pay a 500 dollar pet deposit over time and keep the cats. She agreed. Now we discovered we have bedbugs and he wants to kick us out because of the cats. Isn't that text message he sent a written agreement?