But this is an odd issue: I've never seen the Google button. I just tested this with one of my accounts; I searched for a term, found my client's ad, clicked on the ad, filled out the lead form, got the Thank-you page, and... there was no logo. But the conversion code is embedded in the ASP code, and the conversions are tracked.
I suspect that Google "reserves the right" to display the logo, and they choose not to show it, but they may at some point (or sometimes).
Is there a third-party solution? Is there a way for me to track conversions without any logos (or anything) appearing to the visitors?
In the long run, it's probably best to keep that conversion data out of the hands of the media companies selling the advertising. With a large enough sample size, they know exactly what it's worth and may raise prices accordingly. Just take a look at price increases at Shopping.com.