It still not clear to me: does SSIS connect directly to your site? Or does it connect to a server at the client where it inserts data into a table through four-part notation? That sounds a little funny, but you keep talking about a linked server.

I have never worked with SSIS myself, so I don't really know what to configure there. But common sense tells me that it is just another conncetion string, and you need Encrypt=Yes in the connection string. And you need a certificate that is installed in both places. (Or use the self-signed certificate that SQL Server generates, but then someone can eavesdrop that certificate when it crosses the wire.)

Maybe you should first to get encrypted connections going locally. The simplest is to try SQLCMD with the -N option.