“I sat through a long ‘interview’ full of Hollywoodism’s disrespect and sarcasm — but finally had enough and literally, physically removed my mic and walked out, much to Cohen’s chagrin,” Ms. Palin wrote.

Mr. Rohrabacher and Mr. Walsh, of the “kinderguardians” segment, both described being approached by someone claiming to be from an Israeli television crew looking to interview supporters of Israel for a program about the 70th anniversary of the country’s founding. Mr. Walsh provided emails to The Times that shed some light into Mr. Cohen’s approach. Here’s one:

“Subject: Media Request for Rep. Joe Walsh

“To Whom It May Concern,

“My name is Ashley and I am writing to you on behalf of First Liberty Pictures. We are currently producing a docu-style series that will air on the Israeli network YES and we’d like to feature Rep. Joe Walsh as a “Friend of Israel” since he has consistently been a supporter for the security of the Israeli people. Our show’s aim is to highlight the common security concerns that our countries share, learn from each other’s perspective, and further illustrate the unshakeable bond between the U.S. and Israel.

“Rep. Walsh understands that the post-9/11 security situation in the U.S. is similar to what Israel has faced since its creation, in the form of terrorist organizations like Hamas, the P.L.O., Hezbollah, and ISIS. He understands it’s crucial that Americans are ready to defend themselves against radical Islamic extremists. Terrorism is no longer just in Tel Aviv or Jerusalem … it has spread to places like Orlando, San Bernardino, and Fort Hood, and it’s threatening our shared values of freedom and democracy.

“For the on camera appearance, he would meet with a gentleman from Israel who has seen the tactics used by these extremists up close and has developed unique anti-extremist techniques that very few in the world are privy to and he would like to share them with Rep. Walsh and our audience.

“We’d love to fly him out here to film with us in the L.A. area at the end of October or alternatively, we plan to be in the Washington D.C. area the first or second week of November. Would he be available then? Please let me know his level of interest in participating.

“Looking forward to speaking with you.”

Mr. Walsh said in a phone interview that Mr. Cohen’s team went as far as to charter a limousine for him, provide hair and makeup for the on-camera appearance, as well as present him with an actual award that lauded Mr. Walsh for “significant contributions to the state of Israel.”