wordpress search not returning correct results

I’m hoping someone can point me in the right direction to troubleshoot the wordpress search. I’ve inherited a website where search isn’t working correctly. It returns results that aren’t correct (they don’t have the search word in them) AND even though there are just 7 results (in a particular case), the pagination indicates 33 pages.

I installed the Relevanssi plugin and thought that might fix it but it displays the same results. However, it adds a facility in the backend where you can see search results which is to be used for troubleshooting and that search displays the correct results. The Relevanssi documentation says that this is likely because the theme is interfering.

When this problem first happened, before my time, they were using a different theme. I have since replaced it with another theme and deleted it. I know that the theme I chose doesn’t have this problem as I have set this up on another site and it works fine.
I have no idea how to track down what the issue is – which wordpress files contain the search function? Which files may be interfering? If the theme has been deleted is there any way something may be lingering that is still getting in the way? Any pointers appreciated, thanks!