"Thank you, goodbye!"
Translation:Dziękuję, do widzenia!
It's not among the suggested options, so what was your answer that the algorithm considered "żegnaj" the closest correct option to your answer?
"Żegnaj" is quite like "Farewell", it does sound as if you are never going to see each other as well. Also, the word is similar in usage to "Witaj" (Welcome). They both seem hard to explain in terms of how they work grammatically.
After all, both "Żegnaj" (2nd person singular) and "Żegnam" (1st person singular) can work here. It's a bit easier to show it on "Witaj" ("You be welcome"? No, it's not "You are welcome", it's imperative) and "Witam" (I welcome you). May be really confusing.
Are you sure? In what situation? we do not know the context here. Could you say "cześć" leaving a Post Office, or a Court, or a DMV office? I do not think so. "Do widzenia" is more polite and formal and without knowing the context you cannot just use"cześć" in this sentence.
Frankly, it's hard to answer because I just don't know what made you want to write "po"... the main meaning of "po" is "after", other meanings are easier to discuss on specific examples.
Among the most important meanings of "do" is "to" (a letter to Tom, I am going to the shop), and "until".
"Do widzenia" is like "Until (the next) seeing", so "Until the next time we see each other!"