Good critical thinking, remember from your training that uncured product should never touch the clients skin so no, don't let it cure and file off. The overexposure damage is already done to the client and the product is potentially contaminated with oils, dust and debris that will lead to lifting. I would push the product back to the centre of the nail, working from side to side to keep it even until it started to cure and not run. Or remove it with my brush, not wiping, ensuring that all of the product is removed from my brush before moving on. Make sure to pull the lateral folds of skin away from the moving product. Better, as
@moonails says to inspect your bead on the brush before you lay it down on to the nail, discard if too well (or dry of course)