can bad throttle kill a 3spd. Manul trans?

Look here:  https://www.holmanparts.com/wp-content/uploads/2015/09/12_TVCableAdjustment_V2.pdf

Nick

The goal is to provide enough pressure to keep the slippage in check but supply a smooth shift and not use excessive pressure that can effect mileage to some extent. Older transmissions like the Rambler's has its characteristics "built in". More modern cars control the transmission pressure and shifting with computers and solenoids as opposed to older cars that have the "built in" characteristics decided be permanent springs in the valve body. The throttle valve is the one of the few variables the older transmissions have to do what computers and solenoids do today.

I'll stop here because I've gone beyond simple at this point.

Update: I just noticed that you state MANUAL 3 speed. Since the shift point of  manual is selected by the driver and their foot on the cutch dictates the abruptness, no I can't see a throttle adjustment burning up a manual transmission. That said, what I stated does apply to Automatic transmissions. They can be burned up if the throttle valve is misadjusted and there is internal slippage.