The phrase "not care to" refers to a lack of interest or willingness to do something. There are several synonyms for this phrase, including "not feel inclined," "not desire," "not want to," "not be bothered," and "not be interested in." These phrases can be used interchangeably in order to convey a similar meaning to "not care to." Depending on the context, other synonyms like "dislike," "abhor," and "hate" could also be appropriate. It's important to select the right synonym based on the situation and the intended tone, as some phrases may have a stronger connotation than others.