DAE feel bad for chopping down trees after reading The Two Towers?

You definitely aren’t alone. Tolkien was struck by trees and at had a vivid childhood memory of a great tree he was fond of being felled and left to rot.

If you really feel guilty you can go plant trees to counteract your cuts.

Edit: I can’t find that particular passage, but here’s a great passage about his fondness for one in particular

There was a great tree – a huge poplar with vast limbs – visible through my window even as I lay in bed. I loved it, and was anxious about it. It had been savagely mutilated some years before, but had gallantly grown new limbs – though of course not with the unblemished grace of its former natural self; and now a foolish neighbour was agitating to have it felled. Every tree has its enemy, few have an advocate. (Too often the hate is irrational, a fear of anything large and alive, and not easily tamed or destroyed, though it may clothe itself in pseudo-rational terms.) This fool* said that it cut off the sun from her house and garden, and that she feared for her house if it should crash in a high wind. It stood due east of her front door, across a wide road, at a distance nearly thrice its total height. Thus only about the equinox would it even cast a shadow in her direction, and only in the very early morning one that reached across the road to the pavement outside her front gate. And any wind that could have uprooted it and hurled it on her house, would have demolished her and her house without any assistance from the tree. I believe it still stands where it did. Though many winds have blown since.