Back link to the developer's studio

We are doing now an advertising site for the book. Everything is as usual. Only when I put the reciprocal link to our studio, the customer asked her to remove, justifying it by the fact that the site is advertising and he does not want his site to have any other advertising.

I have this situation for the first time, 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 the customer ask for this link and how to relate to this?

Yes, in order not to produce another topic, I will ask here about SEO: does the domain name influence search engine positions? Suppose the domain name is kupit-mashinu.ru, will this site have more weight if the user's request was “to buy a car”?
')
Thank you all 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 advised to put the author meta tag to get out of the situation.

Using:

 <META NAME="Author" Lang="ru" CONTENT="  , .., _@."> 

Note:
As far as I know, this meta tag does not 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 when ranking the site.