Yes, you can. That technique is called RegEx (for Regular Expression). There are some different 'flavors' of regex depending on what software you are using, but they all generally support the basic commands.
There is a short explanation of RegEx in
MR's Wiki.
You can try:
Search: <p class="calibre_"><span class="bold">Page (\d*?)</span></p>
Replace: (nothing)
Give it a try, one at a time until you are sure it isn't going to pick up something unwanted... then you can Replace All.
As always, save your epub first!
Cheers,