LinkedIn connection wants to send an invoice for ATS checking, cover letter, and profile optimization services.

I received a LinkedIn connection invite from a profile listed as a job search expert/career coach. They didn't offer a job opportunity and only asked for my resume, which they reviewed and claimed was non-ATS compliant and in need of fixing. I didn't get details from them on what specifically was wrong. They offered resume, cover letter, and LinkedIn profile optimization services. The invoice they emailed used my maximum stated budget and cced their personal account officer, both of them gmail accounts rather than a business domain name.

Communication was grammatically correct and professional-sounding, communication was prompt to the minute and took place only during business hours, and they didn't try to move communication to a 3rd party site, aside from the emailed invoice. The profile is LinkedIn verified. It's listed as a Fiverr freelancer, has hundreds of connections, and seems to comment congratulations on job seeker profiles that landed roles (it does not seem to post anything else). I compared the email address in the profile and the invoice, and they do match. But I'm suspicious given the number of scams around. (I've run my resume through ATS checkers before and updated accordingly, so while I would believe if it wasn't perfect, it seems less believable). They are also based in Canada, while I am not.

Is there a good way to identify a scammer or tell if these services are legit? I have of course not touched the invoice until I can verify.