Try:
Sub Demo()
Application.ScreenUpdating = False
Dim Rng As Range
With ActiveDocument
Set Rng = .GoTo(What:=wdGoToPage, Name:=4)
Rng.End = .Range.End
With Rng.Find
.ClearFormatting
.Replacement.ClearFormatting
.Forward = True
.Wrap = wdFindStop
.Format = False
.MatchCase = False
.MatchWholeWord = False
.MatchWildcards = False
.MatchSoundsLike = False
.MatchAllWordForms = False
.Text = "Appraisal Report Number:????????????"
.Replacement.Text = ""
.Execute Replace:=wdReplaceAll
.Text = "Appraisal Item:"
.Execute Replace:=wdReplaceAll
End With
End With
Application.ScreenUpdating = True
End Sub
As for your TOC, if it references content in the body of the document and you delete that content, the TOC, too, will lose those references as soon as it is refreshed. Conversely, a Find/Replace cannot permanently delete content from a TOC; anything deleted from a TOC will re-appear as soon as it is refreshed.