The couple, who last week used the social networking site to rant about how TOWIE producers were "lying" to viewers, took offence to Argent's material about them at a comedy night shown on yesterday's (March 13) episode.
In posts that appear to have now been deleted from Twitter, Falcone wrote: "Find it funny how larg has stuff to say when I am not there to defend myself.... Strange... I have not 'bought' any twitter followers Neither has Lucy....
He went on to stress that "a recent increase" in followers was down to him emailing his contact details to a database of five million people so they could "book appointments with me for a bespoke suit service".
Mecklenburgh added on her own profile: "I can confirm me & @Mario_Falcone have never bought Twitter followers! Is that actually possible?! Unfortunately mario only got an iPod [for Valentine's Day']!"
Argent appeared to respond to the couple's comments on Twitter, stating that they "should be...good sport[s]" about his jokes.
"A roasting is a form of comedy where you take the mick out of people and tell jokes," he wrote. "Should be a good sport and take it on the chin #Banter."
Falcone and Mecklenburgh's fall-out with Argent comes after an unknown TOWIE cast member reportedly told Now that people on the show were getting fed up with "acting like absolute d**ks".
"Unfortunately they're still very important to the storyline, so they get away with acting like absolute d**ks," the star said. "We would all be fired for what Mario said [about producers]."
The Only Way Is Essex continues Sundays and Wednesdays at 10pm on ITV2.
Watch Digital Spy chat to the TOWIE stars below: