she has not consulted us, but the tree root is in our garden. Should she not ask us first if we want them. The twigs and branches had fallen in her garden.

By law she has the right to remove them but since it is your tree she must return them.

If that is your tree messing up HER property then You should clean it up.
That is exactly what I do.....I also did it when the neighbor threw their walnuts into my yard....Solution Throw 'em back.
Sorry.