What was the other third party? I assume the argument will be the airline paid for redundant data centers and IBM didn’t live up to that portion of the contract.
I haven't been able to find the name of who exactly, most articles only mention "unrelated construction work", which is why I made the previous comment, but as the other commenter answered, i guess that would be a separate lawsuit.
Depending on the size of the construction company, any claim made against them will just result in them shutting down and going out of business if their insurance won’t cover it. This is a pretty common occurrence in construction.
If Kyndryl wants to sue a third party to see if they can recoup some of that cost, that's their business.