The screen on my iPhone SE 3rd Gen no longer does a good job of resisting oily fingerprints – suggesting the oleophobic coating has worn away.
From Apple:
Will a good screen protector have an oleophobic coating that can partially restore fingerprint resistance? I have been looking at the FLOLAB protectors which claim to have oleophobic properties. Has anyone used these?
Thanks!
You can buy new liquid coating and apply yourself.
Example
I saw that article and was going to link to it but noticed that it was written in 2012 – although it shows a more recent date. They mention that the coating needs to be reapplied every few months.
Edit to add: the oleophobic fluid mentioned in the article is no longer available.
I don’t have any specific screen protector recommendations, but I do see a fair number of them that advertise oleophobic properties at $5-$20. I’d just try one.
FWIW, I can’t say I’ve noticed dramatic differences between my screen protectors and my iPhone screens, but maybe I eat less pizza than others. 
It was just an Example, I’m sure you can buy it from other places. One of my close friends redid the coating on his 13 Mini a couple of times before he upgraded the phone.
Update.
I bought this one from FLOLAB. It comes with an alignment tool that mostly/sorta works. Once applied, the screen protector works well and resists fingerprints which makes it easier to use the phone outside. The only issue is the iPhone SE3 has a Touch ID which is now slightly recessed owing to the thickness of the cover.
Bonus: when I purchased the item I selected 2. Once in my basket they offered a BOGO (buy one, get one free) offer so I ended up with two for the price of one.