Q. When is the word that unnecessary? Here’s an example: “She manages the team, making sure that everyone is in the right role and that everything is of the highest quality.” Is it okay to remove those thats?
A. More than a few grammatically nebulous constructions are actually cases of omission—or what’s known as a grammatical ellipsis. In the following examples, the brackets supply information that would be understood from context or otherwise:
[It’s amazing] How ugly [that rock is]!
She’s taller than I [am]. (But see CMOS 5.46.)
Why [did you do that]?
Thousands rushed to serve him in victory; in defeat, none [of them did].
Jasper missed her and she [missed] him.
[Would you like] One lump [of sugar] or two [lumps of sugar]?
We made sure [that] everyone was happy.
The man [who is] in the moon isn’t real.
All those sentences make grammatical sense without the bracketed words that might complete them. In some cases the elliptical construction is preferable (as in the proverbial “man in the moon”). The “rule,” if we were to state one, would be simple: Any omission that sounds right and does not obscure or alter the intended meaning is an option.
Your example works well enough either way. If you favor economy, delete the thats. If you think they provide a bit of useful emphasis, keep them. If you’re unsure, try reading both versions of the sentence aloud. For more on relative pronouns and grammatical ellipses, see CMOS 5.226 and 5.229. (For the punctuation mark known as an ellipsis, see CMOS 13.50–58.)