One of the most useful words in English is also one of the most maligned: that. Some writers drop it reflexively, as if every instance were deadweight. At times, omission is entirely proper. After the verbs say and think, for example, you can typically omit it without a hitch: He said the claim was bogus; she thought the claim was well-founded. But a sound instinct in one setting becomes a bad habit in another.
With verbs such as acknowledge, believe, claim, decide, demand, doubt, state, and suggest, the conjunction that is an invaluable signal. He stated that the claim was bogus is better than he stated the claim was bogus: without that, the reader initially expects the claim to be the object of stated. So too, she believed that the leader, a cult founder, was a charlatan is better than she believed the leader, a cult founder, was a charlatan—which may suggest, for a beat, that she believed the leader. The conjunction marks what follows as a proposition, not merely as the apparent object of the verb.
The cost of omission is often a momentary miscue. The board decided the question did not need to be resolved briefly suggests that the board “decided the question.” The state asserted the defense had no merit makes it seem, wrongly, as if the state is asserting a defense. HUD demanded the money be returned to the bank can work, but restoring that signals the construction immediately and leaves no syntactic debris in the reader’s path.
Still, no rigid rule can replace the writer’s judgment. Writing well requires empathy for the reader, especially when the writer is deciding whether to omit that. Omission is often harmless when the subordinate clause begins with a pronoun: ensuring you receive the care you want; he never admitted he was wrong. But when a noun phrase follows, retain the conjunction unless its absence is unquestionably smooth. Don’t delete it willy-nilly. Don’t deny your readers a signpost, a hinge, a moment of instant comprehension. They’ll need that.