Gus,
Thanks so much for providing that link. I followed Step #2 because my problems were one, I could not unlock the phone with my fingerprint and second, could not enroll a new fingerprint after deleting the old.
First I cleaned the home button and surrounding area of the ring real good with a paper towel slightly dampened with glass cleaner. Second, I made sure my finger was clean, dry, and oil free. Then I went into the Touch ID settings and proceeded to enroll a new fingerprint. Once again it stopped and gave me the "try again" error even with a thoroughly clean finger so I had an idea and decided to change the position of my finger from vertical to horizontal. THAT idea worked and I was able to register and save my new fingerprint. The next step, of course, was to see if I could unlock my phone... I did have to try a couple of times but I was able to unlock it eventually. The big difference is that towards the end close to the day I posted here about my problem, I could not unlock the phone with Touch ID no matter how many times I tried!
I will post back here again if my experience reverts back to the same issue.
At first, prior to posting here, I thought my problem may have been due to a hardware issue but I was inclined to attribute it to the system software because as I previously stated, the problem only surfaced after I upgraded to iOS 10.3.3. Before that, I wasn't having problems and I periodically clean my screen with a microfiber cloth on a regular almost religious basis. (Plus I always have clean hands whenever I use my phone). But in hindsight, after reading the Apple Support document, I never cleaned the home button when wiping the screen. Just the main glass panel. So I think that the home button may have just accumulated dust, dirt, and oil over time as I have had this iPhone SE for just a little over a year now. Thankfully I didn't have to do Step #7 because that was my initial solution before I thought to ask on these forums. I was ready to head for the Genius Bar! (I do have mobile insurance for my phone from my carrier so if the problem was with the hardware, I certainly would have elected to make a claim and opted for a replacement device under my plan. At least I didn't have to go that route thanks to you!).
I appreciate you taking the time to check out my post and providing a solution.
Sincerely,
🤓
Pismo 900
P.S. I have to mention too that my iPad mini 4 which has Touch ID, wasn't experiencing any issues after upgrading to iOS 10.3.3 as well (all three of my iOS devices were previously on 9.5.3 before I decided to finally upgrade to 10.3.3 the other week) so I kind of wondered if my iPhone was indeed suffering from a hardware issue!
Touch ID not working correctly after upgrading to iOS 10.3.3