Question: Say you are working in an office where English is not a native language for people but some English terms are used very often (e.g. an IT department). And your boss always pronounces English terms incorrectly.

The question. Is it appropriate to pronounce the terms correctly when speaking to the boss or one should use his wrong pronunciation for any reasons.

It seems to me a bit uncomfortable to use the fixed pronunciation just after his incorrect wording (right in the next sentence). He may find this offensive I think. He may think that I'm either too dumb to remember how it's pronounced after one second after his saying or I'm trying to teach him.

P.S. Trying to tell him how it's pronounced correctly is not an option. Please avoid this advice. Thank you.

Answer: 
This answer becomes trivial if you stop thinking of him pronouncing it **wrongly** and instead that he is pronouncing it **in his accent** which doesn't have to be the same as yours.

I have Australian friends who say "dahta" and "dahtabayse" while I say "dayta" and "daytabase". I don't adjust my pronunciation to match theirs. They don't take my pronunciation as a correction to them. And there are plenty of opinions about how to say GIF, SQL, etc -- tech terms don't always have single pronunciations.

You worry that if he says "do we have the dahta?" and you say "yes, we have tons of dayta" that he'll feel rebuked. Why should he? Different doesn't mean wrong. If you feel funny, take refuge in pronouns (eg it, them) or substitutes (the language, the framework, the platform, the library.) If it's been that recent since your boss said the word, it's available as an easy referent using these sorts of words. 

The only reason to change your own pronunciation is if everyone on your team and in your area says it differently than you (and the inventors, and possibly the majority of the internet) and you are starting to feel bad, not as someone correcting others, but as someone who isn't acting according to the norms of your group. You haven't provided any examples so it's hard to know if that needs to happen in your case.
I'm going to answer this question as the person who mispronounces words. I'm a native English speaker but have started picking up French late in life. I can follow a conversation and speak short sentences. I slaughter the pronunciation of words; a native or fluent speaker can understand me though.

I personally prefer if native French speakers use proper pronunciation around me. **Foremost because I couldn't understand them if they used my own mispronunciation.** A secondary reason is maybe, through some odd osmosis or asking outright, I'll pick up the correct pronunciation over time.