They probably won't go away - OR forget.

The Personal Visit to their office sounds like a good idea.
TRY to reason with them...
Stress that You want to KEEP Eli.

And be sure to point out (possibly show receipts?) that
You paid $160 in Vet bills for him.

Curious - WHAT was the $45 for??

As for the "contract" that says they "own" Eli...
*I* wouldn't argue that point too much -
They just might have a Lawyer that would be willing to take
you into court. That could cost you more than the $45 if you need
to also have an attorney.

Seems to ME that they ought to be Happie as Klamz to forgive the
$45 and know that Lil Eli has a FurrEver home!

Good Luck!!

/s/ Phred