Indeed, as Mister Sparkle said, they do grow back. How well, though, depends on how mangled it became - sometimes they just don't grow back to look how they used to.
As for the filter, I'm sure Sparkle will share plenty of knowledge about the sponge filter. But, should you continue to use your current filter, I might as well inform you that there are other ways of anchoring that curl of plastic. From this picture I stole (http://www.bettafish.com/showthread.php?t=30139
), you can see that Big Oki uses a fishing weight to anchor it, obviously a more stable alternative to most tapes.
That being said, what kind of tape were you using to begin with? I'm sure a strip of duct tape would be pretty solid. Also, I swear I read on here somewhere that somebody uses a plastic sandwich bag. How, I don't know. I could be lying. Maybe a plant below the waterfall would prove more effective.
And lastly, what if you baffled the intake? Wouldn't that lessen the outflow to some degree? And if you raised the water level enough, there'd be almost no current at all, right? You could put a sponge, or pantyhose toe over the intake, as seen here: http://www.bettafish.com/showthread.php?t=35469