Correction : You have to promise NOT to tell anyone about the job offer, though.
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The major usages of though has the following meanings :
AS A CONJUNCTION
1. Despite the fact that; although:
He still argues, though he knows he's wrong. Even though it was raining, she walked to work.
2. Conceding or supposing that; even if:
Though they may not succeed, they will still try.
AS AN ADVERB
1. However; nevertheless: Snow is not predicted; we can expect some rain, though.
2. Informal Used as an intensive: Wouldn't that beat all, though?
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Now that you are clear about the various usages and have seen the examples,
In this sentence "though" Stands for "however"
e.g. (To a colleague) I have a good news. I have got a job offer and am throwing a party. You are invited. You have to promise no to tell anyone about the job offer, though. I don''t want my boss to know about it.