I have trained as a fake white belt in a GTF school b4 in college haha.
Im not very knowledgable about it's popularity in america . As for my country the former representative of ITF Malaysia(Master Sabree Salleh) became the representative of GTF Malaysia. GTF's training and techniques are basically the same with ITF ones. Even their forms/patterns/kata are the same excepting Juche i think.
The only difference is GTF is Founded by Park Jung Tae(former 8th Dan ITF GrandMaster) and is supposingly free from political ideals(i.e. Gen Choi's iron grip i heard)
As far as ideals are concerned, their taekwon-do techniques are refined/enchanced with knowledge of other Martial arts. For example the standard mid section punch of ITF is held straight whereas in GTF it is slightly bent at the elbow. This is to prevent the joint from being easily destroyed by a blow(a derivation of Wing Chun i heard). When i heard this explaination it truly showed me that ITF techniques still have space to improve!. Recoils have been taken out from some kicks i.e. sidekick, turning kick
Sparring rules are the same with ITF and so are 90% of the syllabus .
Hmm that's about it i think. Others may have more info of course, as i only trained there until the school's master literally forced me to reveal my former rank haha. I was not kicked out but staying there as a senior means i don't get to practice as much . wasn't fun barking orders almost every class anyway, so i took off. And that was only 3 months.