This pane of the Control Panel is used for the incremental updates obtained from the web. LTspice is often updated with new features and models. Use the menu command Tools=>Sync Release to update to the current version. If you don't update for a couple months, LTspice will begin to ask if you would like to check for updates. LTspice never accesses the web without asking for your permission to do so. LTspice contains no spyware or transmits any type of data while obtaining the files it need for update.
Don't cache files: Neither cache nor use files cached on our machine for the update.
Don't verify checksums: For security reasons, LTspice uses a proprietary and confidential 128bit checksum algorithm to authenticate the files it receives off the web for updating. This authentication can be disabled in case there's an error in that algorithm. However, no problem with this has ever been reported, so it is not recommended that you ever defeat this security feature.
LTspice uses only high-level operating system calls for its Internet access. It should not be required to make any adjustments to these settings except in rare cases when you need to specify the Proxy server and password since LTspice is not managing the Internet access, but your computer and operating system. Settings on this pane are not remembered between program invocations.