Hmmm. Odd that they don't like the apple tree branches. My guys don't pay attention to softer cardboard items like toilet rolls or egg cartons either.
Other "toys" that my degus like are:
– a cardboard tube covered with alfalfa (by Living World I think)
– straw mats (also made by Living World)
– tunnels and hammocks designed for rats and ferrets
Mostly, my degus like their wheels, sand baths and anything with apple branches. They also like to redecorate their cages by moving around their ceramic food bowls, their wooden huts, and their straw mats. Other than that, they play with each other and get excited by food-related objects like bits of grass and dandelions and clover.