This kind of Kinetic Typography was a staple of the Scala Video Titler for the Amiga, first and of Adobe After Effects for the PC, later.
After a while it became a bit boring because everyone was doing it everywhere, but to see it now, done so well, so much time before, and with only analog equipment, it is really inspiring.
I'd immediately remove every reference to linkedin -anywhere- and hard-block their domain in the code.
Only after, I'd probably seek a release from the injunction.
Perhaps you should involve a lawyer, but if you won't, then limit yourself to a brief matter of fact explanation of what you've changed, focusing especially on the block in the source code.
Do not address their points yourself. Refrain from any commentary, apologies, admissions.