Adding Static Content to Dynamic Index.php

Hi, I’m trying to add a snippet of text to index.php, as a welcome message to the blog home page. I’d prefer not to use the static page option (and I’m on an older version of WP), but rather just want to add a bit of code that ONLY shows up on the index page, not any other pages. My problem is that the code is showing up on all pages, not just the index.

See https://cultivateresearch.com/grapevine/.

I’m hoping the only option isn’t going with a static page and calling the most recent blog posts? Should be an easier way to just add small bits of static content to the existing pages.

Thanks in advance for any help!