If the leak is anything more than just trivial, it needs fixing.
Brake bands will not cause this, they are not even used until it is moving.
Check your fluid level first, is the fluid nice and cherry red, if brown and smells and tastes of acid then the brake bands are starting to break up.
It has nothing at all to do with the brake bands, these just hold clutch drums still when in gear so slippage doesn't occur, but yours is almost certainly a pump/pressure problem.
The brake band is adjusted, if you know what you're doing, if not DON'T, by turning the 3/8 square adjuster sticking out the side of the box, when set correctly the car will free wheel in 4th gear when easing off accelerator.
If the filters never been changed do it now with fresh fluid, you can also get a adjustable vac can for these, improves the shifts, and the valve body parts(valves/springs) can be swapped to make more sporty, as I did, although there is not a specific kit available.
If keeping the car fit a TRANS cooler, after the rad cooling, this cuts down massively on heat, and makes it last longer as well.
I fitted a winnebego motorhome trans cooler and cut 65C temp out, my left foot was roasting on a hot day from the trans heat, this box was designed to use draughted air, in the us cars, but no draughted air provided in european cars so they benefit massively from a cooler.
tabetha