I taking an educated guess (I have no association with the plugin) that the YouTube watermark may be protected by the TOS governing use of the YouTube API. So, if it’s the YouTube watermark, the answer is probably no, but the YouTube T.O.S. might explain it in greater detail.
youtube.com/static?gl=US&template=terms
Section 4, item F, may be the applicable description.
From what I read here:
http://www.reelseo.com/remove-youtube-logo/
Youtube now allows the removal of their logo. I need to add ?modestbranding=1 to the video url, but am not sure where in tubepress to edit this. Could you direct me?
Dashboard > Settings > TubePress > select the Player tab > scroll down to YouTube settings and make sure the check box is selected under:
“Modest” Branding [*] Hide the YouTube logo from the control area.