There is anecdotal evidence of surgical wound cross infection from household pets. Ensure you have clean bedsheets when you return home after surgery and do not allow pets in your bedroom and no cuddles for the first 3-4 weeks!
Once you have stopped using the tape 4 weeks after surgery, massage the scar with pressure using a non-perfumed cream or bio-oil (do not use an old pot or bottle incase it is harbouring bugs, buy a new one!) for several weeks to months, and always use high sun-block for the first year in the sun. Remember scars do take a year or so to fade.