National Forest Restoration and Remediation Act This bill modifies the treatment of monies collected by the United States arising out of certain Forest Service activities. The bill directs the Department of the Treasury to invest in interest-bearing obligations all monies that were previously collected by the United States in forfeitures, judgments, compromises, or settlements related to Forest Service activities, provided the amounts are not required to meet current withdrawals. The bill makes available the interest earned to cover the costs of work rendered necessary by the action which led to the forfeiture, judgment, compromise, or settlement.