I don't think there is an easy answer here besides having to recreate the recurring meeting.
There are a few Google Product forum discussions on the issue, but no good resolution. The only certain fix (for events in the future) is to turn on 1-way sync (Outlook --> Google)
Here is one of the latest threads about the issue (with no resolution).
You can try using this VBScript, but this is not an official solution. I would test this out on a few test meetings first: https://sites.google.com/site/esillybin/code/changetheorganizerofoutlookmeeting (credit: Tom Weber who is the listed author of this Sites post)
Public Sub CalendarRecurringItem()
'Below is just creating variables and declaring their types
Dim objOL As Outlook.Application
Dim objMsg As Outlook.AppointmentItem
Dim objSelection As Outlook.Selection
'Below sets the objects to Outlook and whatever items you have selected
Set objOL = CreateObject("Outlook.Application")
Set objSelection = objOL.ActiveExplorer.Selection
'Below the For Each statement is going through each item you have selected in case you selected more than one calendar item
For Each objMsg In objSelection
'Below is showing you a message box and saving your response in a variable named "answer"
answer = MsgBox("Are you the Organizer of " & objMsg.Subject & "?", vbYesNoCancel)
'Below is going through the three possible answers from the question above
Select Case answer
objMsg.Parent.MeetingStatus = olMeeting 'This sets the MeetingStatus to olMeeting which is equal to 1
objMsg.MeetingStatus = olMeeting 'This sets the MeetingStatus to olMeeting which is equal to 1
objMsg.Parent.MeetingStatus = olMeetingReceived 'This sets the MeetingStatus to olMeetingReceived which is equal to 3
objMsg.MeetingStatus = olMeetingReceived 'This sets the MeetingStatus to olMeetingReceived which is equal to 3
objMsg.Save 'This saves your change to the meeting item
'This clears the variables so you do not mess up anything else by leaving values in the variables.
Set objMsg = Nothing
Set objSelection = Nothing
Set objOL = Nothing