Damage items can be repaired by using Repair skill. Allow each character with the skill to attempt to fix one item between each session. If the damage is moderate, make a simple roll, if it is serious or major, require a raise. If it was truly catastrophic, you may disallow any repair attempt. Some Blue Special Rewards Cards allow for repair or replacement of damaged or destroyed items.
I would think that the damage to the Beast counts as serious or major. So, it would require a Raise. Neither Sister Maria, Captain Freemont, Pumaman, nor Two Chains have repair skill. I don't know about Friday Jones or Rusty Keys.
Eugene has repair d4, Pierre has repair d8. So, each could make one roll, needed a Raise to repair the Beast. (No bennie use between sessions, however, and they don't get bennies anyway).
I reckon that since Andrew is GM next, it's up to him to make the rolls.