Hello Jeff,
I had the same issue, but was able to resolve it. I only had the issue when it came to line and polygon features.
First, make sure all the editing is enabled via the feature layer settings.
Then, navigate to the Field Maps app via Enterprise:
1. Select your field map
2. Go to settings
3. Under Collection, toggle on Delete all Points.
After enabling this setting, I was able to delete features on the map as well as desktop.