Why do search engines put up incorrect links to the site?

Question

Google

We completely updated the site, it used to be on joomla, now it is self-written, but we encountered the problem of incorrect issuance of links in the description and links not to the main page. He directs, almost right, but not quite. When accessed, all requests are sent to index.php, then they fly depending on the url by class and no appeal to index.php smells there (as well as .html, which search engines also add).
It turns out that I have, for example, such a link:
example.com/page1/page2
Google makes a link like this:
example.com/index.php/page1/page2.html
It's clear, it gives 404. What to do with it?

Answer 1

take a proger by the tie
and a SEO specialist - all of a sudden you really have everything right)) and Google doesn’t know how