OK, in case somebody else has similar needs as me, I found a partial workaround for now:  I set the background color, text color and border color all to the same value.  So, now, the flags appear, but the text next to them (that contains the visitor counts, etc.) is not visible to anyone.  I also changed the href code to point back to my site and have bookmarked the original href site so that I can still visit it for my stats, but my visitors can't click on the image to be taken to my stats.  You can see how my hack of the widget looks by visiting http://blogannath.blogspot.com/  .  Thank you.

Thanks for your warm welcome, Grishend.  I understand that not having to register at Flagcounter is an advantage to some people too.  I think it would be a good idea to offer either a visible counter with no registration and also offer some kind of options to keep your stats private by requiring registration.  I hope such an option will be offered in the future.

If we offer a private version, it will be Pro only.  We really don't want people modifying the code like you've described (and this actually is prohibited by our Terms), as this prevents people from visiting our site.  Our site contains our advertising, which pays the bills.  If everyone were to do this, we couldn't offer this service.

I just discovered this service.  It's very cool, and I would like to add it to my page.

blogannath hit my concern on the head.  While it shows number of viewers I won't use it.  If it could be modified to show percentages-only I would love to use this.