Responsibility of a web designer - site may be hacked

A client of mine did a google search for his site and the listing came up with "this site may be hacked" underneath it.!!!!!
I've spent a day trying to find out what this about (via google search console) - I have deleted all the files on the server except the WD files in the public_html folder.
No idea what to do next.
To what degree is a web designer responsible for an attack on a site - is it their responsibility to "fix" this - I would have to get outside help (at my cost?) and have this problem looked into.
Has anyone had a similar experience?

Yes, that happened a while ago to TalkGraphics!

I think there is some way to contact Google and have them check the site again.

The first line of defense is a strong password. And if your web host offers it, two step verification. When you enter your password to access your files your host texts a numerical code which you key in.

Yes, there is a page on webmaster tools where you can ask google to review the site - but only after you have fixed the errors.
I can ask my client to change his password, but I have know idea how to fix the problem - call in a web hacking specialist?

Can you post the url?

Got hold of the hosting company and they ran a complete set of scans on the site - all clean.
My client is changing his password - I will delete all the old files and re-upload them and then re-submit it to google - hope this does it!