How do I care for my yucca that is coming back from the dead?

My yucca plants got very damaged by extreme heat and sun in my conservatory so I took them into the garden, cut off the damaged leaves and just watered them occasionally. I thought I'd need to throw them out but then I went away for two weeks and came back to this healthy looking new growth at the bottom of both plants. I'm unsure what to do now. Do I just leave it be, water occasionally and see what happens (and take inside when the weather cools)? Or should I be looking into some how removing the damaged top part and, if so, where do I cut? Any tips on caring for them now would be appreciated!