Here is the item again:
Scooting the dead cockroach under the refrigerator with the toe of his shoe.
You correctly identified the fragment as a participle phrase. Scooting, the present participle that begins the phrase, is the clue.
To fix this fragment, you could add a subject and verb, like this:
Meanwhile, Marc was scooting
the dead cockroach under the refrigerator with the toe of his shoe.
Or you could use Punctuation Rule 3:
Main clause + , + participle phrase.
The correction would look like this:
Marc distracted Sharon with the benefits of sharing the small
apartment, scooting the dead cockroach
under the refrigerator with the toe of his shoe.
Or you could use Punctuation Rule 4:
Participle phrase + , + main clause.
And the correction would look like this:
Scooting the dead cockroach under the refrigerator
with the toe of his shoe, Marc distracted Sharon with
the benefits of sharing the small apartment.
Enjoy your knight!