If they don't want to walk outside from E to C which I wouldn't blame them in the winter with heavy bags, then a free airport shuttle to Terminal C is the way to go. Massport - Logan Airport - Interactive Map Will show them where to pick up the shuttles. Shuttle Service at Boston Logan International Airport will show which shuttles go where (though pretty much any shuttle you get on at E, will eventually get you to C).

If one didn't have any checked baggage then they could simply go back through either security checkpoint at E and you can walk airside to C.