If the carpet is glued on, a petroleum based solvent will usually dissolve the glue. If you've ever used a product like "Goo Gone" or similar, the primary ingredient is something like kerosene. I have a CHEAP 5 gallon jug of kerosene (I've had for several years) in my outbuilding. I use that for projects like this.
BUT!!! Always TEST an inconspicuous (hidden) area FIRST - let the solvent sit for 15 minutes or so. Kerosene is fairly weak, but it's petroleum based, and CAN dissolve certain plastics. However, I seriously doubt it would harm the plastic engine cover.
NOTE #2: Petroleum products are VERY flammable! NEVER use around sparks/fire etc. AND use plenty of ventilation. Wear protective gloves... it's harsh on your skin.
With all that being said, kerosene is an effective solvent for removing glued on stuff - think of it as industrial strength Goo Gone.