<p>How can I check the umask of a program which is currently running?</p>

<p>[update: another process, not the current process.]</p>

If you're the current process, you can write a file to /tmp and check its setting.  A better solution is to call umask(3) passing zero - the function returns the setting prior to the call - and then reset it back by passing that value back into umask.
The umask for another process doesn't seem to be exposed.