What aircraft "don't respond well to tarmac runways"?
No airplanes absolutely need a grass strip, but for some taildraggers (airplanes which have a tailskid instead of a wheel) it's a real benefit because the grass is softer on the skid, and the friction of the grass improves control on the ground and helps slow the plane down. Pavement isn't that big a problem for skids make from more modern materials, but you can imagine it's not going to do a slab of wood much good. Many vintage designs have no brakes or poor brakes, so having grass makes a big difference when landing, on pavement you'd end up rolling a lot longer and have less directional control at low speed.