From Longman Dictionary of Contemporary Englishnot care to do somethingnot care to do somethingLIKE somebody OR something old-fashioned to not like doing something She doesn’t care to spend much time with her relatives. I wouldn’t care to meet him in a dark alley! I’ve experienced more reorganizations than I care to remember (=a lot of them). → care
Examples from the Corpusnot care to do something• Wyatt's old friends didn't care to visit, with a baby in the house.• He suspected Hubert had erred in some way, but did not care to ask.• It's not something I care to discuss.• Unfortunately, Roth did not care to focus on broader and more important issues about the fate of the seized-assets program itself.• De Gaulle apparently did not care to give ministers an opportunity to make important decisions without his supervision.• But I have to make one comment you might not care to hear: A woman does have a choice.• At least, not precisely in the act of anything Mrs Dallam would not care to know about.• He did not care to know how many female holly trees a single male could bring to berry.• The poets did not care to linger in that gloom-hidden abode.• I would not care to live in the vicinity of such a device.