Trail Stewardship for Economic Recovery Act of 2020 This bill establishes the Trail Stewardship for Economic Recovery Fund. The Forest Service shall use amounts deposited in the fund to enter into cooperative agreements or contracts with an outfitter or guide to carry out on National Forest System lands (1) trail maintenance projects, and (2) additional invasive plant and noxious weed prevention and control projects. The Forest Service shall (1) give preference to projects that can be performed in an area that the Forest Service has selected as a trail maintenance priority area, and (2) expedite projects with the goal of initiating the majority of them not later than 120 days after enactment of this bill. The Forest Service must annually submit to Congress a list of those projects that (1) meet the criteria described above; and (2) have been, or are expected to be, funded from the deposited amounts.