tmpregex

This pattern should do what you need:
<a\b([^>"']|"[^"]*"|'[^']*')+class="changed-by">.*?<\/a>

I tested the pattern here:
https://regex101.com/r/IyL5JR/2/

To use this in VBA you'll probably need to escape the " characters by replacing each one with ""

Based on some example code from here:
https://stackoverflow.com/questions/22542834/how-to-use-regular-expressions-regex-in-microsoft-excel-both-in-cell-and-loops

You could create a function to use from your Excel cells like this:

Function simpleCellRegex(Myrange As Range) As String
    Dim regEx As New RegExp
    Dim strPattern As String
    Dim strInput As String
    Dim strReplace As String

    strPattern = "<a\b([^>""']|""[^""]*""|'[^']*')+class=""changed-by"">.*?<\/a>"

    If strPattern <> "" Then
        strInput = Myrange.Value
        strReplace = ""

        With regEx
            .Global = True
            .MultiLine = True
            .IgnoreCase = False
            .Pattern = strPattern
        End With

        If regEx.test(strInput) Then
            simpleCellRegex = regEx.Replace(strInput, strReplace)
        Else
            simpleCellRegex = strInput
        End If
    End If
End Function

You would use it by putting a formula in a cell like this:
=simpleCellRegex(A1)