I see no reasons to put the list of servers into a dictionary, you can start working as soon as the share path is read from the text file from the ".ReadLine" line.
Below is what you can do. Also, you DO realize that search for these shares WILL take a LONG time to complete if there are significant number of files and directories under the shared folder.
Option Explicit
Dim fso, temp, src, ts, file, shell, fileToDelete
src = "H:\servers.txt"
fileToDelete = "test.doc"
Set fso = CreateObject("Scripting.FileSystemObject")
Set shell = CreateObject("WScript.Shell")
Set ts = fso.OpenTextFile(src,1)
Do Until ts.AtEndOfStream
temp = ts.ReadLine
Set file = shell.Exec("cmd /c dir /a/s/b " & temp)
Do Until file.StdOut.AtEndOfStream
temp = file.StdOut.ReadLine
If fso.GetBaseName(temp) = fileToDelete Then
fso.DeleteFile temp
End If
Loop
Loop