On the one hand, I can see American schools not wanting to lose out on a lot of money and pressuring lawmakers to restrict it to domestic schools only.
On the other hand, I can see depleted economies from war-ravaged allies (and enemies) similarly eager to grab onto that money.
So were there any restrictions on where this money could be used, and was there political pressure responsible for any restrictions?
Short answer is yes.
Although I can't speak to the broader questions, the history of San Miguel Allende in Guanajuato Mexico has an interesting answer to the primary question. San Miguel (now a UNESCO world heritage site) became a center of the arts largely due to the art schools which boomed in the post-WWII period due to the influx of former US soldiers studying abroad under the GI Bill.
The town is a beautiful Colonial Baroque architectural time capsule. It went through multiple boom and bust cycles after it's heyday mid-18thC and by the mid-19thC it was practically abandoned. In a phenomenon that seems to happen all over the globe throughout modern history, a few artists rediscovered the place decades later, stepped into the beautiful-and-cheap-but-neglected void and began to colonize the town.
An art school (Belles Artes) was established there in 1938 and an ex-pat American writer named Sterling Dickenson appointed director. He actively recruited on US campuses after the war. With tuition covered by the GI Bill and living expenses dirt cheap (Dickenson purchased his entire property there in the late 30's for the equivalent of $90US) it became enticing for those looking for an arts education off the beaten path.
If I recall correctly the famous Mexican muralists Siqueiros and Morado both taught there as well as a raft of other literary and visual art luminaries. The town's reputation as a cultural center really took off in the 40's with that influx of GI Bill money and it became a beacon for both int'l students as well as domestic talent.
To make a long story short, many of the students settled there and/or returned for retirement and it's now a fairly cosmopolitan city with a large resident ex-pat population. The thing I find most interesting about it is that unlike almost every other ex-pat heavy town I've ever been to, San Miguel firmly retains its Mexican character blending both the indigenous and colonial cultures in a truly unique mix. It really is a cultural gem that undoubtedly wouldn't have developed into what it is today without those GI Bill students.