Answers
Open the VBA Editor of Excel and type this in the Immediate Window (See Screenshot)
Application.AskToUpdateLinks = False
Close Excel and then open your File. It will not prompt you again. Remember to reset it when you close the workbook else it will not work for other workbooks as well.
ScreenShot:
EDIT
So applying it to your code, your code will look like this
Function getWorkbook(bkPath As String) As Workbook
Application.AskToUpdateLinks = False
Set getWorkbook = Workbooks.Open(bkPath, False)
Application.AskToUpdateLinks = True
End Function
FOLLOWUP
Sigil, The code below works on files with broken links as well. Here is my test code.
Test Conditions
Create 2 new files. Name them Sample1.xlsx and Sample2.xlsx and save them on C:\
In cell A1 of Sample1.xlsx, type this formula ='C:\[Sample2.xlsx]Sheet1'!$A$1
Save and close both the files
Delete Sample2.xlsx!!!
Open a New workbook and it's module paste this code and run Sample. You will notice that you will not get a prompt.
Code
Option Explicit
Sub Sample()
getWorkbook "c:\Sample1.xlsx"
End Sub
Function getWorkbook(bkPath As String) As Workbook
Application.AskToUpdateLinks = False
Set getWorkbook = Workbooks.Open(bkPath, False)
Application.AskToUpdateLinks = True
End Function
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