How can I remove the "apple watch" app, which recently appeared on a home screen?
You can't remove several of the Apple-supplied apps (try removing the ever-useful Stocks app, for example).

The Apple Watch app is one of these.

Generally, people tend to move these to a folder that they use to hide the 'useless' apps, or move them to a different screen - just so you're not staring at them all the time.

Where I live, the Apple Watch is not even available yet, but still I got the app staring at me to remind me of this constantly. It got hidden pretty quickly!