Dear Designtrinity,
This is in addition to what Atul Sharma has said. Most noteworthy point in his post is about being polite.
Secondly, when the company approached you for the interview, why you did not tell them to make arrangement for the air travel? What was hold up? Rather than arranging the air travel, if the company tells the job candidate to make arrangement for the air travel then it throws light on the company's culture. I sense lack of authority of the HR department. HR has played safe by passing the buck to the candidate.
Thirdly about delay in settlement of the TA claim. This happens anywhere and everywhere. Even American MNCs are notorious for the delayed payment. Few MNCs are so process centric that they do not understand that what they call as "being process-centric" is nothing but plain bureaucracy. Therefore, show patience at least for a month.
Lastly, you have written that you have received e-mail agreement for the reimbursement of the airfare. Who has sent the mail? What is the designation of that person?
Final comments: - The delay in settlement of TA claim, tendency of the HR to tell job candidate to make arrangement on his own speaks about company's internal way of working. Even if job candidate is told to make arrangement for the interview, what matters is expeditious settlement of the claim. The incident puts into question image-consciousness of the company.
Hope you have applied for the manager. Is this the way manager should be treated? Therefore, even if you are offered a job you need to take a call on whether to join company or not. An environment of trust is missing in this company, that is for sure.
Thanks,
Dinesh Divekar