I've read in several places that it's better to omit "that" in sentences, because it's best to omit extra words. Also in programs like "Grammarly" and "Pro Writing Aid" they recommend removing it for that reason.
But sometimes it feels/sounds like it's not grammatically correct. Are there rules that govern whether one can/should remove it? Is it a matter of style?
"...the plane Bill had folded..." vs. "the plane that Bill had folded..."