In Tanzania this would probably be tea(Hot water and tea leaves). In Kenya this would be tea(Milk and tea), which is also called Chai. :)
Yes, that's an accepted answer. I still think the sentence is a bit weird though, unless there's some custom I don't know about drinking tea with eggs (raw? mixed with the tea?)
I think they were trying to say "Let them drink with their eggs" as in boiled or fried eggs. The English translation is again very weird.