Courtesy, amenity, attention, gallantry are comparable when they denote a manner or an act which promotes agreeable or pleasant social relations.
Courtesy suggests consideration for others or deference (as to their rank, sex, or age); it usually implies good breeding and acquired graces but it sometimes connotes innate gentleness or instinctive politeness rather than social training.
Amenity implies a disposition to make easy the approach to or the continuance of pleasant social relations; when used concretely it may be applied not only to words or acts but to pursuits, interests, or facilities that bring men into rapport.
Attention implies a singling out of a particular person for special favor or consideration, or as the recipient of courtesies showing one’s admiration or love (as in courting).
Gallantry stresses devoted attention, sometimes amorous attention, to a lady; it also often connotes ingratiating personal qualities (as ease of address, a dashing style, or a polished manner).