If your LinkedIn profile was public before and then you disabled your public profile, your profile picture is still accessible without having to login to LinkedIn. It is not just a caching issue as it is still available from CDN for months after the profile is being made private. The images are loaded from media.licdn.com and will be indexed by Google. Even if you delete your profile picture, the previous one is still accessible from the CDN. When I contacted LinkedIn support for content removal, the person told that media.licdn.com is not associated with LinkedIn and I will have to remove it myself and from the search engine which indexed it. The funny thing being that the domain certificate shows LinkedIn Corporation as the organisation. The whois also has LinkedIn in it.

Domain Name: licdn.com
Registrant Name: Domain Administrator
Registrant Organization: LinkedIn Corporation
Registrant Street: 1000 W. Maude Ave
Registrant City: Sunnyvale
Registrant State/Province: CA

Update: I had it removed from Google search using Webmasters already. LinkedIn removed the image now.