1
general::
Phrase(s): *an itchy palm [and] *an itching palm
Fig. [of a hand] in need of a tip. (As if placing money in the palm would stop the itching. *Typically: get ~; have ~; give someone ~.) • All the waiters at that restaurant have itchy palms. • The cabdriver was troubled by an itching palm. Since he refused to carry my bags, I gave him nothing. • Whenever he sees expensive luggage, the hotel doorman gets an itching palm.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Also, itching palm. A desire for money, greed; also, wanting a bribe. For example, The porter has an itchy palm; he wants a big tip, or The mayor was known for his itchy palm. This expression alludes to placing money in the palm of the hand. [Late 1500s]
American Heritage Idioms