I would leave it for protection! How is the wrap working out for you? My stock header shield is coming loose. Making noise rattles on cold start up! Check cooling fan wiring and cooling fan relay. Connector for relay always go bad. Once it separates completely will put wrap.
The wrap went good, removing the heat shield was a pain and the dip stick tube O-ring messed up upon install, it fits tight now till I can find a new seal. I did this for looks thats all, I had no issues I was trying to solve, but the job came out good and clean. Since I was doing this for pure asthetics I really want to remove those ugly aluminum tube covers.
Good job! Looks cool! I replaced the hose before because it had bubble. New factory hose brings the foil. P/S pump is right there too. So you could try to remove it but just make sure you look at it from time to time.