Backlink to developer studio

We are now making an advertising site for the book. Everything is as usual. Only when I put a link back to our studio, the customer asked to remove it, justifying it with the fact that the site is advertising and he does not want any other advertising on his site.

This is my first situation, so I want to ask: is this normal at all? Does the studio have the right to put a back link to your site? Can a customer ask that this link not exist and how to relate to it?

Yes, so as not to produce another topic, I’ll ask here about SEO: does the domain name influence the positions in search engines? Let's say the domain name is kupit-mashinu.ru, will this site have more weight if the user’s request was “buy a car”?

Thanks in advance :)



Based on the comments, it turned out that the reverse link can be set only with the consent of the customer, unless otherwise provided by the contract.

JetMaster suggested setting the author meta tag to get out of the situation.

Usage:

Note:
As far as I know, this meta tag does not in any way participate in the ranking of the site in search engines (at least in foreign ones. Correct if I am mistaken).

On the issue of SEO, the following was clarified: the domain name still plays a role in ranking the site.