I've never used one myself but I've heard talk of various ones either A) taking the public (real) like number and extrapolating the dislikes based on an old like/dislike ratio available for the video from before the dislike removal (doesn't work on new videos) or B) the extension includes a feature where the user can like/dislike the video within the extension and then the dislike number is extrapolated using the public (real) like number and the extension's private like/dislike ratio. In either case the number is not connected to the "real" dislike count that YouTube would have access to internally