Targeting and Offsetting Existing Illegal Contaminants Act This bill provides for a program within the Forest Service to detect, monitor, and remediate the environmental damage caused by trespass cultivation of cannabis on National Forest System lands and increases criminal penalties for illegal pesticide application on government property. Specifically, the bill directs the Forest Service to carry out a program of environmental remediation on its land, to be known as the Trespass Cannabis Cultivation Site Remediation Program. The Forest Service shall pay fees and charges imposed by state authorities for permits for the disposal of hazardous substances, pollutants, contaminants, improper pesticides, or other wastes on Forest Service lands to the same extent as nongovernmental entities. The Forest Service may enter into agreements with certain entities to carry out the Forest Service's responsibilities under this program. The bill establishes an account in the Treasury to collect amounts recovered from trespassers for response actions, as well as amounts from other sources. Funds in the account may only be used for environmental remediation.