Silly me.
I guess I am just paranoid thinking an app that asks for location permission would ever access your location. We all know large companies like UPS, Facebook or Google would never access our seemingly private information.
What was I thinking?
Well I don't know about your particular phone, but on mine, when an app is using your location (like Google Maps) it puts an icon at the top of the screen. And there is a place in the settings where you can see every app that asks to use the location function and you can turn it on or off. And when you install an app it tells you whether it is asking to use your location. So you have at least three places to see whether an app on your phone is using your location, and exactly when.
And the UPS Go app does NOT ask for permission to use your location. It does NOT appear on your list of apps that use your location. When you use it the location icon does NOT appear on the screen.
Yeah it says it needs access to your location in the description. That is obviously a mistake by a careless IT person and not grounds for a conspiracy about personally tracking your location outside work. Facebook and Google are both apps that follow the procedure of telling you when they are using your location and you can go turn them off right now.
So yes, you are being silly and paranoid. You don't understand what is going on, so you are making up a conspiracy theory to make sense of it. But the simple answer is usually the right one.
By the way - there is one company that is tracking your location that does NOT tell you about it when it happens, and that is your cell service provider. If you are truly worried about being tracked, you need to throw your cell phone in the nearest river and go back to land lines. If you ever have a serious accident at UPS, you can expect that the insurance companies involved are going to be requesting your phone records from your cell provider and checking to see exactly where you were, how fast you were going, and whether you were on the phone or texting at the time. The silly company app, which doesn't know your location at all, is the least of your worries.