When you find large trash items left by others in less accessible places, what should be done?

The exact scenario:
We were hiking a ten mile trail on US Forestry Service land with river crossings and came upon an abandoned tent. It was one of those larger four man, twenty pound tents and damaged beyond use. We do carry bags that we use to ferry out other trash we find but there was no room in our packs for an extra tent.

Edits for clarity: Things that are very clearly trash and fairly large.