Given the links have been created via HYPERLINK it's a little more cumbersome than normal... the quickest fix would be to adjust your formula and remove the optional friendly_name from the function, eg:
=HYPERLINK("The Plots\"&X5&"_TT_"&Y5&".png")
You will find that Excel will at that point use the full link as the friendly_name (display text) by default - and thus you can pull your links by virtue of the cell's value (ie as you are now)
Without modifying the formulae - using your sample - you might get away with using Evaluate to pull the underlying link, eg:
Dim rngCell As Range, strLink As String
For Each rngCell In Range(...to be specified...)
With rngCell
strLink = .Parent.Evaluate(Split(.Formula, ",")(0) & ")")
End With
Next rngCell
or something along those lines...
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