It is not up to Grumman to fix the guns, it depends on what is the problem. Just as it is not up to Grumman to fix engine problems or faulty propeller operation.
The guns are government furnished equipment, or in the case of export planes (commercial sales) they are customer furnished equipment.
The .50 cal ammo used in 1940 used 750 grain projectiles. While undoubtedly destructive if they hit the rate of fire for four .50 cal wing guns in 1940 was 40 rounds per second at best.
The ,303 ammo used 174-175 grain ammo (for ball mmo) but the eight ,303 guns had a rate of fire of 160 rounds per second at best. weight of metal per second is in favor of the ,50 cal guns by about 8%. Hardly a decisive advantage. The ,303 guns actually fire a bit less weight of projectile because the tracer and incendiary bullets are a bit lighter.
in 1940 there were no .50 cal incendiary rounds, BoB eight gun fighters had one or two guns loaded exclusively with incendiaries depending on ammo supply. One gun was generally loaded with tracer and two guns had AP bullets. During the BoB 3 guns could be loaded with ball depending on supply, later in the war ball disappeared as did tracer (for fighters) and AP and incendiary became the standard bullets.
The Martlet/F4F doesn't bring any significant increase in firepower to the battle. we are talking + or -10% or under depending on how we rate the different bullets. This does not take into account gun problems or installation problems (heaters, feed rollers, long belt feeds, etc).
The Martlet I, II and F4F-3A all perform a bit worse than the Hurricane I. The F4F-3 does have a slight speed advantage (perhaps 15mph) at certain altitudes. It has a lower ceiling? or perhaps about equal.
Even if used it is hard to see any difference in combat effectiveness over the Hurricane I at the time of the BoB and it is easy to see several potential problems.