I know that acces time of a file only gives a mere indication but ik could help a little bit. On linux (and aix) you could use the touch command to save the timestamp in a temporary file. And restore it afterwards.
like:

save_command = "touch -r '{}' /tmp/timestamp.save"
rest_command = "touch -r /tmp/timestamp.save '{}'"

run(save_command.format(<jar_file>))
<do the check>
run(rest_command.format(<jar_file>))

I tried to patch the code with this but I can't. And I don't really now if it is a good idea to do that anyway
FYI i wrote a run function in python.