Hey there,
Your description makes the project sound simple, so I'll keep the price nice and low until I know more about it.
It is not possible to remove a logo and see what used to be behind it before it was added.
I can however get rid of any logo by using one of several methods, the results can be one of the following:
-Blurred out logo (you can see there's something there but you don't know what)
-Mosaic censor (often used on tv, has that pixelated look they use for naked body parts)
-Patched over (I'll cover it with whatever is immediately around it, very camouflage-y)
-Patched over with blur (makes the patch mentioned above less obvious)
*If the logo is just letters, I can even patch up the individual letters so it won't look like a box shaped censor.
If it's too hard to understand, send me over a 5 second sample of the vid and I'll make an example of those choices.
Thanks,
Josh G.