They do monitor major Apostate Websides. Just to remind you watchtowerquotes.ca that they close it. The most funny thing was that the webside DID NOT say anything negative towards the WT society, but only quotes from the early days of Russell, unitl now!!! The excuse that WT's lawyer use was that it could be "misleading to the current teachings"of the WT.....!!!! Yeah showing all the stupid ideas, false prophecies, flip flop doctrines they had over the years it could be "misleading"
Indeed WT is monitoring the major websides, even they have Bethelites trained for "guarding" bible studies that came across to apostatic material. Usually the Bethelites take over the BS in this case so the person who conducts the BS will not fall into more "apostate material and lost the faith". I know this from first hand, but I cannot reveal any more informations about this matter.