Have her sign your release of liability in exchange for the payment. You shouldn't have to cover the ear infection unless it was caused by your pet.
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If you're going to ask the owner of the other dog to sign something already, you could consider adding a provision confirming that the amount offered (and presumably received) represents full and final satisfaction of all claims, known or unknown. Of course, check to local counsel re: relevant statutes or considerations.
Pay nothing without obtained a signed, full release in exchange for your payment.
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