Here is the fragment 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!