as amused as I am in you using a Trademark case to make a point in a small claims post
First, I was pointed to that case by an evidence casebook which references it to show exactly what I used it for! LOL. What makes you think that an evidence ruling in a trademark case can't be used as precedence in non-trademark cases?
And I would suggest you try to update your library. Rule 407 is not solely inclusive of only product liability or personal injury actions. Or I guess you'd suggest that with adoption of Rule 407 the exclusions of inadmissibility have been vanquished since the new rule makes no mention of such.
In language you MIGHT understand, Federal Rule 407 applies to garden variety negligence cases as well as it does to product liablity litigation
Second, this is pure nonsense. You completely misunderstand Rule 407 and when it's used. I take it you haven't yet completed your evidence course, "counselor."
A subsequent remedial measure is an action that a person takes after an event to reduce the likelihood of that event's reoccurrence. How does this apply in the OP's case? How does handing the OP a check ensure that the vet won't lose dog's in the future? In short, just what the hell are you talking about?
No, I think you should reread both rule 407 (not relevant) and rule 408 (relevant), and you will see that in all likelihood, the OP can use the check as evidence against the vet, as well as the statement "we're even."