Hello tjhart7,
Thank you for using Apple Support Communities.
Since you're unable to delete the 2 text messages no matter which delete method used, restart your iPhone if you haven't done so already.
How to restart your iPhone X, 11, 12, 13, or later
1. Press and hold either volume button and the side button until the power-off slider appears.
2. Drag the slider, then wait 30 seconds for your device to turn off. If your device is frozen or unresponsive, force restart your device.
3. To turn your device back on, press and hold the side button (on the right side of your iPhone) until you see the Apple logo.
Also, make sure that you're using the latest iOS version: Update your iPhone or iPad - Apple Support A simple restart and having the iOS up to date can help resolve issues.
Should the issue still persist after these two steps, contact Apple Support for further help.
Cheers!