When Lion-O summoned the Thundercats, the Eye of Thundera gave all of them, except Snarf, the strength and ability to overcome the effects of the bracelets.
Goof: Just before Lion-O summons the Thundercats with the sword and is trapped in a pink beam being shot at him from Mumm-Ra's hands, the Sword of Omens is already full size with the Eye of Thundera showing. Yet just before that moment and just after when he starts the call, the sword is properly small with the Eye closed.
Enslaved by Mumm-Ra, the Thundercats eyes glow red and are capable of shooting out a red laser beam from them.
Mumm-Ra enslaves the Thundercats with the help of metal bracelets like those used on Snarfer by Rataro in The Feliner, Part 1. All the Thundercats except for Lion-O wore one on their wrist and Snarf wore one on his tail.
Mumm-Ra: That piece of tin (the sword) won't harm me.
Lion-O: But the horror of your own reflection will.
Mumm-Ra: Oh! Unlike those miserable Mutants, Lion-O, I learn from my mistakes. (puts shades over his eyes) There is no reflection. Nothing can save you now.
(As the Thundercats attack Lion-O)
Lion-O: I will not use the Sword of Omens against you. You are my friends, and nothing Mumm-Ra can do will change that. I must help you, not destroy you.
Lion-O: Oh, hi, Snarf. I guess you didn't find [the Thundercats] either.
Snarf: (under Mumm-Ra's spell) Oh, I found them all right. And we'll all do Mumm-Ra's bidding.
Lion-O: It's almost daylight. Let's go rescue them.
Snarf: Last time I saw them, Lion-O, they sure didn't look like they wanted to be rescued.
Lion-O: That's only Mumm-Ra's spell, Snarf. Those guys are Thundercats, and nothing Mumm-Ra can do will change that.
Mumm-Ra: Ancient spirits of evil, transform this feeble Berbil into the one creature on Third Earth which the Thundercat Panthro fears, the energy bat!