It's possible she has a garbage can as a PWP or just a garbage can in her house. In New Leaf, you can actually use the trash cans to throw things away instead of paying Reese to get rid of them for you.
unless they are trash (and Resse wont buy them), i just try to sell everything to her...
PS: sometimes, I wonder how she got all these bells to buy all our stuffs...
anyway, for pitfall seeds, i usu try to give away as present to my villagers.. doubt they know its 'usefulness'... they usu happy receving any gifts....