Interesting... What year is your Traverse?
I have a few thoughts about what I might do.
I would remove the screws in that hold that side of the bumper cover in place and pull out that side of the cover. Most bumper covers hold in place at the top with a tabs that fit into slots on the bumper cover.
I would verify the condition of the closest set of tabs on that corner to ensure that they are still in good condition.
Then I would look at the slot in which the tabs fit, to verify their condition.
If a tab or related slot is are not properly locking into each other, this would cause the cover to pop-out slightly in that area.
The bracket with the tabs below the headlight is easy to remove and replace, only a few screws. The slots are part of the bumper cover and are hard to fix without replacing the bumper cover.
Odds are that a tab was broken during initial installation. This would explain why it is not holding correctly.
If you are concerned about rubbing parts removing paint, purchase 3M transparent automotive tape and apply it in any areas where painted parts rub.
I have removed and installed bumpers covers are numerous makes and models of vehicles and they are all basically the same.
See install, removal video here: