1.Did you apply for the job for which you have got call letter for the interview now while serving the PSU which you had joined under compassionate ground?
2. Assuming that you had applied for the prospective job after joining compassionate appointment, then you should have applied for the prospective job through proper channel. In the alternative if you had applied for the prospective job before joining the compassionate appointment, then your attending the job interview by informing the present employer and taking NOC from the present employer is the best solution.
3. Instead of abandoning the job you had got on compassionate ground, better to approach the HR Department of the PSU with your resignation letter now and request them to relieve you from the services of the PSU forthwith, since you had served the PSU for only a month and normally for an unconfirmed employee notice period will not be insisted upon. If the management does not relieve you immediately you can request the management to issue an NOC for the moment to enable you to attend the interview for the prospective job. By following this you will also get your salary. You can provide a Medical Certificate for the abandoned period to the PSU which provided you the compassionate appointment.