Yes, the estate will need to remain open to receive the tax refund and distribute that to the estate beneficiaries.
The executor/personal representative should have been able to request that no taxes be withheld to avoid having to deal with tax withholding that cannot be credited to the beneficiaries on Schedules K-1, but it's almost certainly too late to do anything about that now since the plan has made the distribution and has withheld the default 10% in the absence of any instruction not to withhold taxes.
Depending on the timing of estate income and whether or not the estate's tax year has already been established by filing the estate's first Form 1041, the estate could potentially use a fiscal year to cause this income to appear on a Form 1041 for its tax year ending in 2024.
