Review the original item:
For two weeks, Todd refused to go to his accounting class because Professor
Gastineau would not allow students to wear hats,
under no circumstance would Todd allow anyone to see how badly the
barber had butchered his hair.
You wanted to fix it this way:
For two weeks, Todd refused to go to his accounting class because Professor
Gastineau would not allow students to wear hats under
no circumstance would Todd allow anyone to see how badly the barber had
butchered his hair.
To delete the comma between hats and under would cause an equally bad problem, a fused sentence. A fused sentence occurs when you have two complete sentences joined with no punctuation whatsoever. For two weeks, Todd refused ... begins the first complete sentence. Under no circumstance would Todd allow ... starts the second complete sentence.
The spot between hats and under needs a stronger break than blank space.
You might want to consult the rules for fixing comma splices and fused sentences.