Critics of AmTrust Financial Services Inc., which is being probed by a regulator and pressured by investors, say they have been approached by a series of purported overseas consultants dangling enticing offers. Afterwards, the critics discover these people aren’t who they say they are.

Chris Irons, an analyst at research firm GeoInvesting LLC, which has published several reports critical of AmTrust’s accounting practices, said he was contacted in July by a woman who identified herself as a London-based consultant to a European software multimillionaire seeking contributors to a new investment website. He agreed to meet at a Philadelphia-area restaurant.

At the dinner, Mr. Irons said, the woman, whom he described as gorgeous, plied him with drinks and slipped in several questions about critiques of AmTrust and its accounting methods. “It was the second or third follow-up question on AmTrust that gave me a lot of pause,” he said, adding that she “laughed at many things I said that probably weren’t that funny.”

But the name the woman gave—Diana Ilic—appears to be a pseudonym. The email address she used with Mr. Irons links to a domain name established a few days before the meeting. The London address for her consulting firm turns out to be a mailbox drop.

A woman who made initial contact on social media on behalf of the purported Ms. Ilic doesn’t appear to be who she said she was either. The social-media pages under her name used photos of another woman, a French retail marketer. The purported Ms. Ilic didn’t return phone calls or emails to the contacts provided to Mr. Irons.