I need to find a string within the website files. Specifically looking for the footer HTML files

Question

I've been asked to change part of my client's website which has their social media icons in their footer. They're using WordPress, and while I'm very familiar with editing footer.php or the footer widgets, the HTML in this footer file is in neither one of them. I can't find it in any other files I've looked in, and none of the plugins have any of that functionality.

I figure if I can search all of the website files for the HTML code that's in the footer, I'll find the code and be able to update it. I checked with FileZilla, but it looks like I can only search by file title with that.

Any ideas? I heard that searching by grep is a possibility, but do people still do that?? And I've never done it. Here is a link I saw it in: Grep to find a file that contains a string in a directory

Thank you ahead of time!!!!