The term "courtesy lime" refers to a lime wedge consumed by a smoker to mask the taste of cigarettes before kissing a non-smoker. The lime wedge is placed between the teeth, lips sealed around the rind, and pressure and suction are applied to extract the juices. Most people do not bite off nor consume the meat of the fruit as one normally does with an orange wedge.
The use of lime wedges for this purpose is said to have developed from the traditional salt-liquor-lime tequila shot. It is also similar to dropping a lemon into a festering garbage disposal to freshen the air.