make off with

Reader's　Digest ３・４月合併号の記事 "Operation: Find Avery " からの引用です。

Raquel Witherspoon, 38, was frantically searching for her daughter's Yorkshir terrier, Avery, in June 2022 after making a shocking discovery. Doorbell camera footage showed a young woman with dyed-red hair creep onto her front porch, throw treats to Avery, then make off with the tiny dog.

文脈からして上記の句動詞、"make off with" の意味は持ち去るに違いない。辞書で確認します。

・Oxford English Dictionary: to steal something and hurry away with it: Thieves made off with $30 000 worth of computer equipment.
・Collins Dictionary: If you make off with something, you steal it and take it away with you.: Masked robbers broke in and made off with $8,000.
・Farlex Dictionary of Idioms: To escape with someone or something that has been stolen, snatched, etc.: The thieves busted the ATM and made off with the cash inside.

"with" 無しで "make off" だと逃げ去るだけです。