The web sponsorship gives them greater exposure and ownership than a banner ad. Since you've plugged your site on TV, the client benefits from a true 360-degree ad campaign. I can't stress how important this is. When you sell an ad package, make sure you itemize how much money goes to the web. I don't care what the client sees, but make sure your internal invoices give the web its due credit.
Many TV stations give a banner or two away as an added bonus for a TV commercial buy.
You need to account for the value of your website. If sales is giving the web away, you're worth nothing. In today's trying times, you need to quickly shore up the business case for your TV website. Traffic doesn't matter anymore. Short-term revenue is everything.