The Group is made up of the grid's powerful 'big five' teams and, for historic reasons, Williams, who recently vetoed FIA president Jean Todt's plans for a 2015 budget cap.
Force India deputy Bob Fernley told the Guardian that the big teams also receive the lion's share of the commercial revenue distributed by Bernie Ecclestone.
"We have a situation where we have enriched and empowered five teams and disenfranchised six," he said.
Germany's Sport Bild suggested that the letter, described as "explosive" by one team insider, made clear the small teams' belief that the Strategy Group could be contrary to European competition law.
Now, the London newspaper The Times claims that European Union officials, specifically the competition authority, are "monitoring" the situation.
"A full (EU) investigation would throw F1 into turmoil, potentially wrecking agreements and finishing any prospect that the sport could be floated on the Singapore Stock Exchange", correspondent Kevin Eason said.
Eason revealed that "two people close to the sport" have already been interviewed by European officials, who are "said to be showing concern".
They are reportedly also concerned about the FIA's current role, after a previous EU investigation ruled that the governing body not be involved in F1's commercial matters.
The Paris-based federation is yet to comment.
"We simply cannot run a sport like this," said Fernley, who will be at a crucial meeting involving Todt and Ecclestone in London on Thursday.