Translation:Please do not leave the company yet.
The やめる in this sentence is 辞める, which means: to resign; to retire; to quit; to leave (one's job, etc.)
The やめる in most other sentences in this course is 止める, which means: to stop (an activity); to cease; to discontinue; to end; to quit; to cancel; to abandon; to give up; to abolish; to abstain; to refrain.
The kanji makes them easier to distinguish, but I doubt native Japanese speakers would be too confused if you used the latter in place of the former.
It's okay, but sounds a little unnatural (in my opinion as an American English speaker). "Please don't quit your job yet" would be the most natural sounding translation that keeps やめないで as "don't quit", but it loses a lot of the original sentence. (eg. adding "your" and swiching "company" to "job") I think their translation is the most natural sounding while minimizing changes to the sentence.
I put the same thing (and got counted wrong). I fully agree that there is a distinction in meaning between "Please don't hand in your letter of resignation" and "Please stay late and work some more hours without extra pay."! But without more context, it seems like Duo is asking a lot of us to distinguish between the two concepts. Lerosbif said above that やめる means to quit permanently - an important distinction - but Duo and the hints do not provide us that information.
If かいしゃ is the whole company, what word describes "the office", ie the physical location where you have desks and water coolers and all that?