The only way they display this information is if you (a) add it to your profile, and (b) make that information public.
If you use LinkedIn to tell people when your birthday is - and I have no idea why you would, given its intended use case - then that's your doing, not theirs.
In the "Additional Info" section, either set Birthday back to "Month..." and "Day..." or click on the icon next to it to reduce its visibility to only your network or connections. Then click the "Save" button.
They only know that data because you put it there in the first place.
If you don't want it available - dont put it on the Internet.... is this really such a hard concept to grasp?
The only way they display this information is if you (a) add it to your profile, and (b) make that information public.
If you use LinkedIn to tell people when your birthday is - and I have no idea why you would, given its intended use case - then that's your doing, not theirs.
Use this link to edit your profile:
https://www.linkedin.com/profile/edit?trk=tab_pro
In the "Additional Info" section, either set Birthday back to "Month..." and "Day..." or click on the icon next to it to reduce its visibility to only your network or connections. Then click the "Save" button.
P.S.: You can always lie about your birthdate.