Bradford had been told by FIFA to pay a £250,000 development fee, with that amount reduced to £185,000 after an appeal to the Court of Arbitration for Sport.
The fee was brought down as Stewart was sold as a senior player rather than as a youth prospect. Falkirk fear that could set a damaging precedent and inhibit clubs that concentrate on youth development.
"We feel we're more or less being forced to sell players rather than waiting for compensation," said David White, Falkirk's general manager. "Clubs like Bradford will be tempted to take the case to CAS to get the fee set by FIFA reduced."