A told B: Take off(to mean "remove") the grill,I have to clean it. I looked it up online.
Is the use of "take off" instead of "remove" natural?
Yes, in many contexts, "take off" can substitute for remove:
Before we start the MRI, I'm going to need you to take off/remove all jewelry and anything metal on your body.
To fix the regulator, you first have to take off/remove the protective cover.
One exception is for something like edit, in which case use "take out":
Before we release this year's corporate report, please take out/remove any references to the previous CFO, since we don't want to remind anyone of that scandal.
The process takes out/removes the particulate matter from the solution, so that it may be easily refined.
There may be other exceptions as well.
Take off X means remove X from something that it is on. Usually it is used in the context of clothes. (Take off)
So you can take off clothes and jewellery because you previously put them on (they are on you).
A grill is supposedly an inherent part of a bigger thing (cooker, or barbecue), not just something that is put on something else. In that case, "remove" is more appropriate.