An organization has been sending me what they term "relics" of a saint. It is a small square of cloth encapsulated on a small plaque of the saint. I do not wish to receive these items, sent to solicit money, but I am reluctant to throw them in the trash.

It sounds as though you were describing the third-class relic. A first-class relic is some part of the body of a Saint, usually a fragment of a bone or perhaps a lock of hair. A second-class relic is some article owned by a canonized Saint, usually an article of clothing, or some other personal object associated with the Saint. A third-class relic is something, usually a cloth of some sort, which is merely touched to a first- or second- class relic. 
 
One may serenely dispose of third-class relics. Most piously and properly, this is done by burning or burying it. Merely pitching such things in the trash is probably to be avoided, though there is no absolute Church norm related to the disposal of third-class relics. 
 
The practice of mailing, or placing these third-class relics in the hands of the faithful may, at times seem annoying. But here too there are no absolute Church norms forbidding such a practice, or of mailing third-class relics. This is quite different from first-class relics, wherein significant church norms and laws are involved.