According to their website this popup message can be turned off: http://tapatalk.com/faq.php
It also only prompts a new mobile visitor once anyway, not every time they visit the forum.
From their site:
Q: Why a pop-up is shown in my mobile browser?
A: After you installed Tapatalk, a one-time alert will be shown to mobile web users to notify the Tapatalk option. While you are free to remove it during installation, it is important for us so to keep this service sustainable and free of charge to forum owners.
In my humble opinion, the benefits massively out weigh the down sides. I use Tapatalk on lots of Forums and I really like the interface on both my iPhone and iPad.
For me the best feature is having push notifications sent to my phone of PMs and replys - it means I can turn off the email updates and reduce the amount of email clutter I get. No mobile theme can do this (AFAIK)...
I admit that the app is not free but it is only a few dollars, and if you spend a lot of time on Forums it is well worth the purchase in my opinion.
I hope the admins will consider adding it.