My ruling on the "throwing a ball down the gutter to clear a pin" during a tournament would be a verbal worning or yellow card. Doing stupid things like that COULD put the centres equipment at risk. The ball or the pin could potentially kicked up out of the gutter and go into the masking units or the machine at any combination of angles.
Professionalism. You want Tenpin Bowling to be regarded as a sport? Treat it like a sport. Even if there is no specific ruling regarding the matter itself, it would be very easy to call penalty on the bowler for misconduct and would likely be a verbal warning.
At league level, I would simply ask the counter staff to suggest to the bowler a more appropriate way to deal with deadwood. If the counter staff did not act on the issue, I would assume the staff of the centre do not care what happens to the equipment. Then the next time my bowling ball comes back damaged in that centre, I would know why.
It would also be a stupid thing from the tournament bowlers point of view with the risk of damaging your bowling ball.
Then we talk about the opinions and possible scenarios extending from the issue. What happens if a bowler bowls a shot to clear this aforementioned deadwood, but "accidentally" still keeps the ball on the lane? Then tries again? Makes a bit of joke of the sport to any potential spectators.
Moral to the story, don't do stupid sh1t on the lanes, and throwing the ball down the lane "just to clear some deadwood" is a stupid action. It is something I expect from a 6 year old during disco bowling not from a grown adult playing competitive tenpin bowling. You know that SPORT.......