David Cuthill was telling us:
David Cuthill nous racontait que :

These hidden (hidden because they start with an underscore) bookmarks are
usually added when cross references, links or TOC are added to the document.
Sometimes when you copy/paste between applications, the source or the
destination is marked with a bookmark. I haven't had the inclination to
study this, so I do not know why, but it has never caused me, or anybody I
have heard of, any problems.

I used your code on my Word 2003, and I did not see those hidden bookmarks.
As a suggestion, try to use With ... End With Statements in your code. It
executes faster and makes it lighter to read. For example, your code could
be written as:

'Do not forget to Dim and type your variables...
Dim oWordDoc As Document
Dim TabCnt As Long
Dim Rng As Range

Set oWordDoc = ActiveDocument
With oWordDoc
   TabCnt = .Tables.Count

   For i = 1 To TabCnt Step 4
       z = CStr(i)
       Set Rng = .Tables(i).Range
       With Rng

'Why Copy? You are not pasting it anywhere, are you?
'Maybe the answer to your question is in the code you
'obviously snipped out... Are you pasting?
'If not, what are you doing?
'If so, see my comments above
'            .Copy
           .Collapse wdCollapseEnd
'            .InsertAfter "" & vbCrLf
'Why the "" ? It does not do anything..., I replaced this by this line:
           .InsertParagraphAfter
           .Collapse wdCollapseEnd
       End With
       .Bookmarks.Add Name:="BarChart" & z, Range:=Rng
   Next i
End With