A script could check and set the value of a global variable to tell if it had been tapped before.
If [$$TappedBefore ]
//code to remove timestamp here
Set Variable [$$TappedBefore ; value: "" ]
//Code for first tap of button here
Set Variable [ $$TappedBefore ; Value: True ]
That did it!
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You'll need to be careful that the global field isn't left with the wrong value after a single tap.
Make sure to clear the variable as part of whatever operation is done just before you insert a photo so that it doesn't think that the previous insert is the first "tap" on the button.