See what I did there?
So what's the rule, then? When should you leave it in? According to Daily Writing Tips, here are several things that you should keep in mind. Gosh darn, I can't help it.
When To Keep
Here are some excerpts from the article:
--"How does one decide whether to keep or omit that? Clarity is the main consideration. Will the reader understand the sentence without it? Some readers may stumble over a missing that."
--"The following verbs should be followed by that:
--"A writer’s preferred style is another determining factor....A writer may feel that a sentence flows more smoothly with that than without it"