Yes.
The resources (images, javascript files and such) used by the Box belong to the intellectual property of the respective Box Developer. Proper attribution must be displayed on your site. A link to his website or TBP website is recommended. An exception will be that the developer charges a fee for your usage of his Box in your website, in which case, you are allowed to remove the attribution.
Under normal situations where you use the Html Solution, you will not be downloading any resources into your machine. Thus, there is no copyright issue to deal with. However, if your site is a commercial, or profit-based, you have to read the Box's description to find out if the Developer has a policy of charging a nominal fee, even if you do not download any resources into your machine.
For Drupal users who want to use the Box for the Panel styles, TBP by default grants permission for anyone to download the Box's zipped file, which contains the relevant resources to build the Box, and to only use it on sites which are non-commercial based. Commercial or profit-based sites have to read the Box's description to find out if the Developer has a policy of charging a nominal fee.
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