The mummy wrapping doesn't help. It makes you see invisible, but you remain invisible yourself. Your options:
1. Give up on the arena quest. Probably the best option. The only quest from Thrundarr that you need to do to dive deeper into the dungeon is the "Portal" quest, and it does not in any way depend on the arena. You will miss out on a few nice rewards, but that's it. On the upside you will be invisible for the rest of the game, that's pretty nice.
2. Poolsip to become visible again. Beware that this is dangerous: you can become doomed, or you can lose teleport control and gain teleportitis. Uncontrolled teleportitis is terrible. But if you happen to have sold a blink dog corpse to a shop, and you have enough piety to remove dooming, it's safe.
3. Drink potions of visibility. Unfortunately, those are rare and you might need quite a few of them to last through 20 arena fights. Probably not possible.
You steal a scroll labelled HITME. The orc hits you.