It's not GTK that's going to help you, but standard C functions (assuming your'e working in C). In the callback for a button click or whatever you want to launch your command, you can use popen:
Code:
FILE *fp;
gint exit_status;
gchar *command = "/this/is/the/script";
/* execute command */
fp = popen(command, "r");
if (fp == NULL)
{
g_print("Error running %s", command);
}
exit_status = pclose (fp);
g_print("Script exited with status %d", exit_status);
That's just off the top of my head so you may have to dink around. Do a google search for popen for more information.