Simply put, the SAT won't have you decide whether an answer with or without the word "that" is correct. The reason is they are grammatically identical.
Example:
The school Jack attends is excellent
is identical to
The school that Jack attends is excellent
When the SAT does test you on answers with and without "that," the incorrect answers will be wrong because of some reason OTHER THAN the fact that the word "that" is or isn't there.
For example, an answer may be wrong because of a misplaced comma...
WRONG: The school, Jack attends is excellent
WRONG: The school, Jack attends, is excellent
CORRECT: The school that Jack attends is excellent
I hope this helps!
Thanks for the great questions! Keep asking away
You Got This!
Jin