Thank you for the good work that you are doing.
Is this sentence right or not?
Welcome to the forum, Entofsez.
It is correct.
Maybe "the" doesn't need? Maybe just Thank you for good work that you are doing?
Or "job" instead of "work"?
Whether you use 'job' or 'work', you need 'the'.
And is it also right to use it like Thank you for the good work you are doing? Without "that"?
But what option is more competent and the best to use?
They are all good. Take your pick.
***** NOT A TEACHER *****
You have asked for an opinion, so here is my opinion.
I do not think that you can go wrong (especially in business communications) if you always choose the more formal style.
So I would write something like:
"Thank you very much for the excellent work that you are doing."