Tumah and Korbon Pesach

Someone asked me an interesting question – we see that by the korbon Pesach in the Midbar the Bnei Yisroel were not tamei (since it was necessary for some to have a Pesach Sheini). How about in Mitzrayim? It seems that there was no halacha against being tamei while eating the korbon Pesach in Mitzrayim. Why not? Was it because tumah hutrah b’tzibbur, was it a special din by pesach Mitzrayim that tumah didn’t apply or maybe b’chlal there was no din tumah/taharah before Matan Torah.

Interestingly, if you look in the Chiuch and the Rambam you don’t see any special commandment not to eat the Korbon Pesach b’tumah. The way the Rambam formulates the halacha it seems the only reason not to eat the Korbon Pesach b’tumah was because in general all korbonos are not allowed to be eaten b’tumah. The only thing Pesach Sheini was m’chadeish was that if someone was tamei and couldn’t eat the Korbon Pesach he had a way of making it up.

It could be that since b’etzem there is no special halacha of tumah that applies to a Korbon Pesach so if before Mattan Torah there were no dinei tumah or taharah, then it wasn’t necessary for B’nei Yisroel to be m’taheir themselves before eating the Korbon Pesach in Mitzrayim.

Does anyone have a rayah either way if before Mattan Torah there were any dinei tumah or taharah,