which and that are both correct.
I don't think you really need our help on this. You just need to have more confidence in your own writing. But if you really want to know:
The cat, which was sitting in the tree, miaowed.
Here, the sub-clause sitting in the tree gives you extra information. The commas around which was sitting in the tree show that you could delete the sub-clause, and the sentence would still be valid:
The cat miaowed.
For this kind of sub-clause, which we call non-restrictive, you should use which.
Now compare to:
The cat which was sitting in the tree miaowed.
The cat that was sitting in the tree miaowed.
Here, the sub-clause specifies which cat you are talking about. If you delete the sub-clause the sentence is no longer valid. It is called a restrictive sub-clause.
In a restrictive sub-clause, that and which are both fine. Some of the more prescriptive style guides recommend that you should reserve which for restrictive sub-clauses, but that is really just a matter of taste.
MS Word's style checker follows these more prescriptive style guides, so when it sees a which it assumes that you are using a non-restrictive sub-clause, and insists that you add commas. Needless to say, MS Word is wrong.