How do you automatically remove this data?

You can the below workbook in the Worksheet Object.

 

so whenever you enter new data in Column B and if any of the value in column B exists in Column A. it will automatically delete the duplicate from Column A.

 

Private Sub Worksheet_Change(ByVal Target As Range)

If Not Intersect(Target, Range("B:B")) Is Nothing Then
    Application.EnableEvents = False

Dim rowLoop As Long, foundRow As Long, test As String
  
  For rowLoop = 1 To Cells(Rows.Count, "B").End(xlUp).Row
    test = Cells(rowLoop, "B")
    
    foundRow = 0
    
    On Error Resume Next
    foundRow = Columns("A").Find(test).Row
    On Error GoTo 0
    
    If Not foundRow = 0 Then
      Cells(foundRow, "A").Delete xlShiftUp
    End If
  Next rowLoop

    Application.EnableEvents = True
End If

End Sub