Will absence of reliving certificate create problem in joining public sector banks

When you apply for a new job then most of the times due to advantage of earlier job experience in getting the new job you mention it. Once you mention that you were employed elsewhere earlier then naturally the experience certificate from that would be asked. If you do not mention then nothing would be asked. Choice is yours. The idea of the experience certificate or relieving certificate stems from the fact that you left the earlier department gracefully and did not have a misconduct there. If you cannot produce a document to vouch for your good tenure there then no company would like to hire you now. So while applying anywhere do not mention anything which you cannot substantiate without documents. For example if you say that you had got an annual merit award for outstanding work then everyone would ask that certificate and if you cannot produce it then it would be taken as misleading the current selection committee. So while applying anywhere you have to mention only what you have documents to get verified later.

It is always better to have relieving certificate from a company where you worked for some time and coming back. But in your case, it is only a one-month experience. Did the company give any appointment letter and what are the terms and conditions? Are you having all the original certificated with you? When you applied for a post in a bank did you mention anywhere that you worked in a company for one month and claimed that experience, These are the issues you have to study?
In your case,
The tenure of your work is just one month and it may not add any value to your candidature. So you need not mention anywhere that you worked for one month. Actually mentioning that worked for one month and discontinues may give some negative thoughts to the employers. So it is better to be silent and better not to mention this experience in your CV.
I hope that you have all your original certificates of educational qualifications, nativity, date of birth etc with you and you have not submitted anything in original to the textile company in which you worked.
Did you mention about your job in the application of this job? If you mentioned that you are working in that company at the time of your application, then the bank may ask for the relieving letter. If you have not mentioned, they may not ask you the relieving the certificate.

It is always better to mention the past job which you have undertaken from the previous employer. If such an entry has been made in your application, it must be supported by the prevous experience certificate no matter the tenure was of hardly of a month followed by the relieving letter of the ex- employer. The present employer may make further query about your aquiantences with the job in precise so as to be familiar with your mental frame and intelligence.
If the papers are not ready by the time you are attending the present interview, apprise the present employer of producing the same at the time of your documents verification.
If you are thinking to ignore your one month experience, you may do the same without making indication in your resume. You will have to remain alert during the interview process and your response must be impressive to satisfy the interview board.

As far as HR principles of any concern the joining and relieving of an employee should be proper in order to get the routine proper. If you are not getting relieving order from the ex company whether small or big, it seems to be that you are still working in that organisation without salary. And if you take up another job without relieving (assuming that the new company is waiving your relieving formalities), you are in a position of doing double employment which is illegal according to your ex company. In that case if the ex company came to know about your working with another company, they may sue in the court of law. It is better to get relieved from the ex company by giving proper resignation letter and notice pay if any. It is good for you even if you are not joining in any organisation. Submitting resignation is not a problem to any employee as no organization will lose anything on accepting your resignation provided if you are not handing over your liability to employer.