Is it a light colour carpet? if it’s just one little spot, and you have some off cuts of the same carpet… a last resort could be to surgically cut out a square with a sturdy craft knife or similar where the spot is, and insert a plug cut from the spare bit, with a bit of glue on the underside.
Ruffle it up a bit once dry, and trim the pile down with some nail scissors if it stands out too much, so it blends in with the rest of the carpet.
But when you say
There is a reasonable about of chain marks on the house carpet.
It’s not sounding very promising for that kind of botch…
Probably time to start planning
A) pricing up new carpets
B) exit strategy