From my reading of the LG G Watch User manual pdf there reading of the LG G Watch User manual pdf there are 2 sets of data that can be brought up from a 'Swipe Up' action.
Google Now. This can be customised through the 'Wand' Icon in Google now, and swiping away cards will often give the prompt "Do you wish to continue to receive updates about < whatever >? I doubt this is what you are referring to.
The actual settings/options. There is no mention here or anywhere else as to customising these options. I can't imagine you'd be allowed (or want to) remove something like "Pairing" or "Display" options for obvious reasons, they seem to apply the same rationale to all options, as is standard on all Android devices.
If, on the off chance, you are referring to the app drawer, then you would have to uninstall the app from your phone first as the Android Wear app synchs all compatible apps.
Finally the only other thing I can think of is Notifications you don't want. In this case:
- On your phone open the Android Wear app.
- Touch the Settings Icon
- Touch Mute Notifications#
- Click the + Icon
- Choose what app(s) you want to mute.