Contract variation Dog

I cant see how to vary the clauses in the body of the rent now specimen contract - basically I have agreed with prospective tenant his dog and it appears prohibited in the contract - can I simply offer a side letter clarifying my agreement to this variation? thanks

Does the contract term say something like no pets without the landlords consent which will not be unreasonably withheld? If it doesn’t have that caveat, it may be unenforceable. If it does, a side letter should be OK. Are you sure though? Pets can cauaea lot of damage