I deleted a number of photos without backup more than 30 days ago. Do you know of any legitimate apps that can restore this data?

There are no legitimate or illegitimate apps that can recover what no longer exists. However, there are many ways of preserving photos and videos. Did you do any of these?

• emailed, texted or messaged the photos to friends or family
• iCloud photo sync
• Manual iCloud backup
• Automatic nightly iCloud backup
• iTunes backup
• Transfer your photos to your computer via USB cable
• Sync to Google Photos
• Sync to some other photo archiving service such as Shutterfly
• Sync to Dropbox
• Sync to box.com
• Sync to Microsoft OneDrive
• Sync to Amazon Photos
• back up to Livedrive
• Backup to any other backup or archiving service
• Transfer them to a Flash drive through the lightning port on your iPhone, using a product such as SanDisk 64 GB iXpand Flash Drive Go - Apple

A final option is if you synced your photos to iCloud, you have a Mac, and you use Time Machine to back up your Mac automatically, you can open Time Machine and restore the photo library to an earlier date. To do this on your Mac open Finder, then click on Pictures in the sidebar and launch Time Machine. Go to a time before the photos were deleted and restore

Photos Library.photoslibrary. (If you had ever changed the name of the photo library restore that file instead).

If the answer is no to all of the above your photos are gone forever.