Garmin Connect drains battery of iPhone rapidly

Try restarting both phone and watch. I have been using Garmin 5+ and IPhone for a few months, and no such drain. My stats for 7days are <10%, which considering I never switch it off, I think is fine. I don’t tend to use my phone for videos or even music...So mail and Safari are the battery hogs for me.
At times in the past, I have seen that the BT connection to the watch is not there, and then there is more drain. But toggling the BT switch on the phone always corrects this.
My feeling is that it is an Apple, rather than a Garmin fault.

I had similar issues with my 5 but they haven't been as bad with the 5+
Do you use a third party watch face? Try using one of the standard watch faces and see if that helps.
In the app forums there's a suggestion that some third party faces require constant BT connection to the connect app and it's causing rapid phone battery drain

Why can‘t notifications be sent to the Fenix 5plus without having to run the app in the background all the time??
Really, Garmin is driving me crazy!

You don't need the Garmin Connect app to run in the background on iphone to see notifications or calendar alarms on the watch!

You need it to sync activities, for 'find my phone' (to hear sound on the phone in addition to the colored circle on the watch), for weather etc...

Have only had GC drain a couple times and in these instances it appeared to be trying to update something on the watch. Restarts as already recommended cleared it up. No such drain with GC just open. I keep mine open as I reference it often. Also, sometimes my watches (F3, F5, F5+) stop showing notifications, and I find forcing a sync with GC clears that up for awhile.