Can I un-restore an iPhone 5c?

I have read a lot of these questions, and the answers all say no unless you have them backed up. I accidentally reset my mom's iPhone and everything was deleted, and she didn't have anything backed up. I feel 100% terrible, especially because she had pictures from Rome that were like a once in a lifetime kinda thing. Are you absolutely positive I can't get them back somehow?

Nope. Unless you backed up everything it is impossible. Sorry. In future situations always back up your phone. My photos are all saved to my Icloud, Google Drive, My Mac and my phone so I can never lose them.