There is a handy free video processor that everyone should have in their kit called VirtualDub. It has several internal filters and many 3rd party filters that are all free and rival some of the commercial packages out there. (The most famous one is probably DeShaker which will steady shaky hand-held footage) One of the filters you can get is called logoaway another is DeLogo. Both of those will remove a logo by combining the pixels around it to blend it into the background. I’ve used logoaway v2.4 with good results.
~jr
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