The staff at Royal Liverpool University Hospital and Broadgreen Hospital missed out on the payment because they were employed at the time by facilities firm ISS.
The striking workers' contracts were transferred to the NHS on 1 April 2023, one day after the eligibility for the payment expired.
Kerry Nash, GMB senior organiser, said: ‘NHS workers put themselves on the frontline during Covid and yet they're missing out on this payment.
‘They do the same work as many who have received the payment, the only difference is a name on their uniform or payslip.
‘Their work is vital to the safe running of our hospitals. The least they deserve is fair treatment.'
The walk-out followed strike action by over 200 workers employed by private contractor Medirest at King's Mill, Mansfield Community and Newark Hospital on Friday 17 May after they failed to receive the bonus granted to their NHS colleagues.