TPR piping has one solitary purpose, and that is to relieve pressure should a problem arise that overpressures or boils water in the heater. Such a problem could include the city supply overpressuring for some reason. The discharge will be steam or water, and it needs to discharge somewhere (preferably: safe).
The discharge could be massive since it is fed off main supply.
Even if a bucket met statute, it would quickly overflow and cause a flood event in your home, and that means you'd get to have the guys with the industrial dehumidifiers come out and spend a week busting out drywall and flooring, and unfinishing your basement, then fun with the insurance company. Goodee.
So that piping should "go overboard" to somewhere non-destructive, like a downspout on a downhill side of the house.
The only bad thing about going upward is after the event ends, stagnant water could be trapped in the rise. The installer should have never installed your water heater oriented like that. But these events are quite rare, and are usually the death rattle of the water heater, so I wouldn't worry about it too much.