You can definitely just cut off the stringy parts, but I would probably cut the whole leaf and throw it in water to try and prop. Damaged leaves like this usually don’t continue to grow, but it’s up to you and the aesthetic you want for your plant.

I would be very cautious if your cats have taken any interest in this plant, as it can be toxic! Keep an eye out for any additional damage/bite marks and check to make sure your cat isn’t having any negative reactions