A feminist cookie is the term for the reward some men seem to be seeking for saying or doing something feminist. (There are equivalents for, eg, white people and being anti-racist or straight people and being anti-homophobia.)
Asking someone if they want a cookie may be used to mock, more or less gently, such attention seeking. A man congratulating himself on very elementary good treatment of women (for example "I saw a pretty woman, and I didn't yell at her or try and touch her!") is especially likely to be ungently mocked for cookie seeking. In general feminists consider basic feminist behaviour as essentially a matter of etiquette: it is not a cause for general congratulations and acclaim.
Academically it’s related to Bourdieu and his conception of capital, which is generally formulated as something we can access and wield to better ourselves (social standing, economically, …). In this case it would be a form of social or cultural capital. This concept has also been used to describe the differences in types of capital that are used between gender and sexual divisions, e.g. in the social arena of clubs and evening entertainment most women rely on physical capital or corporeal capital to gain status (i.e. via their looks and fashion choices) whereas men generally gain status through their access to social capital, such as running events, being a band member, such that men hold most social capital positions.
Cookies (or rather, pictures of them) are now sometimes also used as gentle rewards for truly difficult allied behaviour, in particular challenging other men about sexism.