So he [Pharaoh] said to them, "So may the Lord be with you, just as I will let you and your young children out. See that evil is before your faces. Not so; let the men go now and worship the Lord, for that is what you request." And he chased them out from before Pharaoh. (Shemos 10:10 & 11)

The Riva, one of the Bali Tosafos explains: Why did Moshe and Aaron wait by Pharaoh to the point that they were thrown out?

Since Moshe and Aaron were called in by Pharaoh, who was a king, they did not want to leave until Pharaoh gave them permission.

The sefer Chidushi HaLev explains that from here we learn the importance and obligation to always have proper manners (derech eretz). Pharaoh was a wicked cruel murderer who rebelled against G-d. Moshe and Aaron could have walked out as dignified leaders but they choose to sacrifice their honor and be embarrassed for the sake of having derech eretz.

We are obligated by the Torah to have proper manners no matter what the circumstances are. Even if we are degraded or embarrassed we always need to behave correctly.