Reducer will take off that adhesive. Soak a spot with a rag and scrape with a new putty knife, Working it away from your new putty in one direction. Goo gone works well too beings how its an acetone base, but would probably cost more due to the large acreage involved, both are relatively safe, However due to the chemical nature you will need to turn off your furnace (and pilot light) first .... Paint stripper works very well too, Unless you can get adequate ventilation down there I think Jennifer would refrain from such a caustic approach.