iPhone SE Photos; cannot delete photos after backing them up.

Try using the app Image Capture that's in the Mac's Applications folder. You may be able to trash the unwanted pictures with that.

Did you look at the link that vast1 suggested? I hadn't looked at this before (because I don't transfer with a cable,) but this looks interesting. It says this:

If you add photos to your iPhone or iPad by connecting your device to your computer, you can't delete them directly from your device in the Photos app. If the Trash button … is gray when you try to delete a photo from your iPhone or iPad, you might need to stop syncing photos from your computer. Learn how to stop syncing photos from your computer.

This sounds kind of ominous to me. Check out the link it references and see how that applies. I think, mainly, it says "you really ought to be using iCloud." It's them, not me. But I have to say, I like using iCloud Photos, and it seems that's the way it's going…

I'm thinking that you are not using iCloud Photos, but instead you are transferring pictures using a cable; is that right?

Pictures transferred by cable are shown by Photos, but they're not really "owned" by Photos, so Photos can't delete them. If pictures are transferred by cable, then they need to be deleted the same way.

Maybe try restarting the phone and ensure you it's not connected to the Mac when you try to delete the photos.

Cheers

Maybe this can help: Delete photos on your iPhone or iPad

Off the subject, perhaps, but I've just got to comment on "delete photos after backing them up."

If you delete the pictures, then your "backup" is not a backup-- it's the only place with the pictures, and it's vulnerable. When we make backups, we make a second copy so that, if one of them goes to the big computer port in the sky (is no more, has ceased to be, bereft of life, rests in peace, begins the Big Sleep,) then we can use the backup, instead.

If you delete photos after backing them up, then you have no backup.