Step 1 – ask the interior designer for the work order/brief that was provided to them asking them to do the work, i.e. the contract.
If there isn’t one, then they may have some difficulty in claiming the money.
Note that the terms of any contract determine who owns the work.
Step 2 – check with the strata manager whether there are minutes/a record of the previous EC resolving to retain the interior designer to do the work, including the amount of money.
Step 3 – if there is no record of it, then it is a question of whether the EC and/or the Chair had the authority to instruct the interior designer. If they didn’t, then they may be personally liable for the account (if that account is valid).
Does the OC have a provision in place limiting the amount of expenditure that the EC can authorise? This is a standard resolution at every meeting. If there is a limit in place, then they didn’t have the authority.
From what you have said it sounds like the Chair was acting on their own, in which case that person may be liable for the account, if they didn’t have the authority.
More generally, it sounds like the interior designer is having a bit of a try on. $20,000 is a lot of money if there is no scope and no agreement in place. I have a friend who is an interior designer and if you are going to charge that amount you would have a full scope of works with a quote, including the terms, that you would then get the other party to sign before you went ahead with the work. The fact that they did the work is irrelevant, someone could come along and paint a building without being asked to and then send a bill if that were not the case.