Interesting law.com article, Writing Better Briefs: That vs. Which, by Kenneth F. Oettle:

I stumbled on the preferred usage of that and which, probably in Strunk and White’s Elements of Style, which says, "Careful writers, watchful for small conveniences, go which-hunting, remove the defining whiches, and by so doing improve their work." (4th Ed. at 59).

The oft-stated rule for using "that" and "which" as relative pronouns is that the clause should be introduced by "which," preceded by a comma, if you can omit the clause "without materially changing the meaning of the sentence." If you cannot omit the clause without materially changing the meaning of the sentence, then use "that" without a comma.

I do not find that explanation helpful. A lawyer should use words only if they add meaning. Otherwise, the words are just filler. If the words add meaning, then omitting them changes the meaning of the sentence, presumably materially, whether the words are preceded by "that" or by a comma and "which."

The best I can do in terms of articulating a rule is to recommend using "that" when you wish to distinguish one item from others in the same category, as in "the appeal that was dismissed," which tells the reader that other appeals were not dismissed. If you say "the appeal, which was dismissed," then the reader understands that you are speaking of only one appeal. If you say "the appeal which was dismissed," the reader doesn’t know whether you can’t punctuate correctly or whether you mix up that and which.