I know this is an old thread but still wanted to reply incase others are experiencing similar. If you're using a mouthguard I should imagine this could be why the gel is coming into contact with the gums. I would suggest people use a custom fit whitening tray and maybe even cut the gum parts away so the tray covers only (and all) the teeth, so if you accidentally put in too much gel or whatever and it goes onto the gums you are able to get your tooth brush to wipe away the gel from the gums because they wont be under a mouthguard/tray.
Braces were fitted in late 2010. Still currently in braces.