We now have the definitive answer. No more mystery, folks - at last! It's true: Hans says "TLER". He says it very fast and very loud, so it sounds kind of like "klop". Hans is too lazy a fellow to say all of "Heil Hitler", so he tries to make it sound as though he was saying it, by joining in at the end of the ritual and just saying the last syllable. It's the same principle as just saying "cher" instead of "Good Morning, Teacher" with the rest of the class at school.
We have now confirmed this in two ways: first, the subtitles in some of the foreign editions show it as "Tler". Since the subtitlers often are working from the scripts, we suspect they know what they're talking about. And secondly, and even more definitively, Sam Kelly himself wrote me to say that he said "Tler".
The endless rumors about what he was saying ("klop" or "klach") were wrong, as were the rumors about why. He said the rumor about him refusing to say it because he was Jewish was particularly silly - he said that's part of being an actor. He wouldn't get very many roles if he went around refusing to say lines because they were offensive. The other theories ("it sounds like boot clicking", "he's saying 'gleich' which means 'same' or 'me, too'", etc) never really made a lot of sense to me, but until we had proof, I listed them all. Now that we know what's what, I'm happy to post this final, definitive answer for everyone to know! Hans says "TLER"!