As BMIR are not taking over Eastern Airlines there is no legal basis for them having to take on any Eastern staff. They may choose to as an act of goodwill with airbus and eastern, or because it makes the start up easier, but they are not required to. TUPE only applies in mergers and take overs. This is neither. It is a contract that has been won by a different supplier.
Eastern's contract has run out and BMIR have won the new one. In the same way that I chose to shop at Waitrose this week as opposed to Asda. I didn't oblige Waitrose to employ the Asda check out girl who served me the week before. Same rule apples.
It is not a company take over just a change of a contracted supplier. Hopefully Eastern still have work elsewhere for those affected and BMIR will hopefully at least take the local CC even if they can't take the FD.