A tympanic tickle is likely a type of sexual act Ferengi can perform on one another. When performed incorrectly, it can result in an infection in one's lobes. As the techniques involved are unique to Ferengi anatomy, most non-Ferengi are unaware of the tickle's existence; however, Federation doctors can cure the infection with antibiotics.
Quark once received a tympanic tickle from someone (likely a dabo girl) who lacked the necessary experience, and Dr. Bashir had to cure the resultant infection. When the doctor, who was unfamiliar with this term, asked what it was, he quickly answered his own question: "Never mind. I don't want to know." (DS9: "Afterimage")