Hi there.

Might be a stupid questions but did not found the answer clearly.

As people have to resolve Symbols on Kept Dice after keeping their dices (yes, just to be clear), you can be compromised on your check BUT still keeping dices with Strife symbols, right ? You simply won't be able to do that on you next check.

Am I right ?

Correct. You kept the dice already. You choose the dice and you resolve them later. So, if the amount of strife is going to compromise, it’s only going to happen at the last step of the check.

Your interpretation is correct.

A relevant part however is that while it all happens in the last step (6, Resolve Symbols on Kept Dice), it happens in a specific order. First come Explosions, specifically the exploding bit, not the success bit. You roll additional dice and choose whether to keep them. These dice can also still include strife.
Second comes Strife - before Opportunities and then Success. Which means that in a Duel, if you become Compromised from the Strife you get, the Finishing Blow interrupts before you get to opportunities and success!
Technically it could also mean that if being Compromised affected the TN of whatever you are doing, you would be Compromised by the time you get to checking for success.