Do credit card companies ever check up on your web login answers?

No, they do not verify those responses. They are security questions used only to confirm your identity during transactions. You will be asked to correctly answer one or two of them before accessing your account information.

I rarely give my real info for security questions. I do record my answers in a notebook that I keep in a drawer.
Even if give the right answer it is spelled wrong.

If you like, you can make a long code word and use that for one or all of the questions. there is no reason they need to know your mother’s maiden name.

Mother’s maiden name is a security question that predates digital information. I used my mother’s maiden name when I opened my first savings account in 1960.

@Yetanotheruser I never (rarely) give my mother’s real maiden name. I do give a name, but it is different for different sites.
People put too much real info out on FB. You never want the answers to your security questions to be on a site where others can see it.