Authorities say the vandals sprayed the swastika on the shelves back on October 9 around 8:15 p.m. at the Target on Pond Path in Centereach.
The men fled in a black pickup truck.
Suffolk County police are offering a $5,000 reward in the case.
Anyone with information about these incidents can contact Suffolk County Crime Stoppers to submit an anonymous tip by calling 1-800-220-TIPS, texting "SCPD" and your message to "CRIMES" (274637) or by email at www.tipsubmit.com.
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