Word Press Files In My Public Html

Please could I get some help. On Monday I asked my host provider to assist with changing my domain name, after the change everything seemed to work ok but then my host provider told me I needed to do a search and replace and amended something so I could get into the WP admin to use a plugin. I now have a load of WP files in my public HTML and my home page is directed to a WP template. I have told my host provider that I use Sytist for my whole site and didn't think the WP files should be there, their response was: "The issue is caused by the htaccess file. You mentioned to take out anything directing to WP.
In this regard, can you please confirm if the Wordpress installation is required and if we should remove it on our end instead?"  I really need some help with this incase they remove files that are needed. 

Sytist has nothing to do with wordpress. Those wordpress files would be there because your host automatically installed them. 

They should be removed and have them make it so they aren't installed again.

For the index file, download this zip file, unzip it and upload the index.php file into the public_html folder overwriting the existing one.

Thank you for your help, the web host followed your instructions and all seems to work now.

Tim:

Thanks for this. Wordpress suddenly starting showing up on my home page as well. I downloaded the zip file and replaced the php file and all is well again.