The grand reopening of iconic Italian eatery Babbo erupted in chaos when a giant, inflatable rat stationed outside got stabbed — sparking an NYPD raid of the posh restaurant as cops searched in vain for the perpetrator, The Post has learned.

“Scabby the Rat” — the towering mascot long used by unions to protest businesses that don’t use organized labor — was brought to crash the Greenwich Village hotspot on Monday night by Unite Here Local 25 to protest the new owner’s worker policies.

That was while the restaurant’s new owner, celebrity restaurateur Stephen Starr , was inside welcoming guests to celebrate his revival of the legendary pasta destination, which shuttered years ago after its founder Mario Batali got mired in sexual misconduct allegations in 2017 .

“I got there around 6:

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