I would wait till you rack to secondary or whatever you decide to do and take the opportunity to clean the blow-off tube. I'm guessing you might find that it isn't really burnt. Only one way to find out though.
You'll be perfectly fine. I once accidentally dropped my stainless steel thermometer in with 30 minutes still remaining in the boil. I couldn't get it so I left it in and nothing turned out bad. No off flavors or infections that I could notice.