How can I save my mussels? For the record this is my first post here, so hopefully it is on topic I do mean the fishy kind, not the strongman kind:

I bought a kg of mussels but I have never cooked them before so I asked the guy in the shop, the basics and went back to cook them. However, I mistakenly chucked them in a simmering pot without checking and then realised that I need to pull the bits of stuff off them! I didn't want to take them back out in case they were still half alive or something so I have left them to cook. 

I am wondering if it will be ok to cook them till they are cooked and then drain them, clean them and put them in some fresh water with some garlic and butter to cook again (straight away after that) or if I have foolishly missed my only chance to cook them properly. If the latter, can anyone advise on how I should have gone about it (I think I should have pulled the bits off - should I have rinsed them or would that be too cruel?)

I don't want to waste a kg of mussels but I preference this to food poisoning so experienced advice would be welcome! Thanks.
Short answer:  It is safe, although by far the predominant practice is to remove them before cooking.

This is, of course, assuming the "bits of stuff" you refer to are the beards of the mussels, which they use to attach themselves to their growth substrate.  



According to ISSC, International Shellfish Safety Conference, you can leave the beards attached if you wish (emphasis added):


  HOW SHOULD FRESH MUSSELS BE HANDLED STORED AND COOKED?   
  
  Mussels
  should be scrubbed with a stiff brush or coarse sponge and rinsed with
  cold water to remove any debris. Beards can be removed or left
  attached.


Lesser quality sources concur:

According to Blue Ocean Mussels, you can remove the beards after cooking--assuming the bits of stuff you refer to are the beards.

According to Yahoo answers, its safe but I give them little credence.



Here is one article at The Kitchn describing how to prepare mussels and clean them, with photos, in case it helps in the future.  They also note, by the way:


  The beard isn't harmful or inedible (just not particularly desirable
  to our taste buds), so don't fret if there are a few little threads
  left that you can't grasp.