Yes, if the Current Period & Quarter To Date headings are in column  H, the macro
won't work as intended. Here is a revised version:

Sub Macro2()
Dim MT As Integer
Range("I3:M3").Select
Selection.Delete Shift:=xlUp
Range("H4").Activate
MT = 0
Do While MT < 10
If ActiveCell.Value = "Quarter To Date" Then
ActiveCell.EntireRow.Delete
MT = 0
ActiveCell.Offset(-1, 0).Activate
ElseIf Len(ActiveCell.Value) = 0 Then
ActiveCell.EntireRow.ClearContents
MT = MT + 1
End If
ActiveCell.Offset(1, 0).Activate
Loop
Columns("H:H").Select
Selection.Replace What:="Current Period", Replacement:="Quarter To Date", _
LookAt:=xlPart, SearchOrder:=xlByRows, MatchCase:=False, SearchFormat:=
_
False, ReplaceFormat:=False
Range("A1").Select
End Sub