The Battery Cover and Glove Box are retained by use of a "Captive Boss",
Triumph Part Number T3351111. They cost GBP £3.65 each :

The "Captive Boss" clamps around a partial cut out in the the upper Fairing :

The Battery Cover or Glove Box are then located above the Captive Boss
and a Fairing Bolt is inserted to secure it in place :

The Fairing bolts should be tightened to JUST 3 Nm

( Which is NOT very tight at all ! ).
IF they are overtightened, or the bolt is allowed to corrode in place in the Captive Boss,
then it is LIKELY that the three small spot welds holding the Captive Boss components together,
will break apart when you try to remove the screw

.....

This
can then mean that the only way of removing the cover, is to destroy it by cutting it off !
The Captive Boss cannot ( easily ) be accessed from underneath.
The
Spire Bolt type section of the Captive Bolt remains sandwiched around the Fairing Panel,
while the head of the "Boss" part remains in place and just spins freely when you try to unscrew it.
Attempts to remove the parts forcibly can also result in damage
to the Fairing panel where the Captive Boss is sandwiched.

Worse case scenario : New Captive Boss @ £3.65, New Battery Box Cover @ £25.00 approx,
and a new Upper Fairing Panel kit : Approx £210.00 = £240.00 Approx !

Add another £10.00 approx if it's the Glove Box that has to be replaced !
Moral : DON'T overtighten the securing screws ! ! !
( And a bit of grease on the threads will help too ! )
Cheers

