Here is the sentence:
Scrubbing the tile grout with bleach and an old toothbrush, the mildew stains
began to fade.
Good choice! You recognized that the modifier is dangling. Scrubbing the tile grout with bleach and an old toothbrush, a participle phrase, has no target in the sentence to describe.
To fix the problem, you should revise the sentence like this: As Michael scrubbed the tile grout with bleach and an old toothbrush, the mildew stains began to fade. Adding Michael to the sentence lets the reader know who is scrubbing the tile grout.