If it's not copyrighted media, then use a garbage matte or track matte.
If it's copyrighted, do you have permission to use it? If so, ask the media owner to remove it.
Very simply, put one copy of the video on track one and one copy on track two.
Blur the heck out of the video on track two and either use the Crop effect on the blurred video to get it to cover just the logo, or a Garbage Matte as Peru Bob suggested.
However, the reason for the watermark may be to prevent you from using it, as Peru Bob also suggested.
Unless the creator has specifically waived their legal moral rights (a part of copyright law in many countries) you could be legally liable for removing their attribution (moral rights).
That's a legal claim that arises in addition to any copyright issues that ensue.
I watermark video that I puiblicly post. I remove it and provide copies to those who shoudl have that right.