Think and decide sincerily. Dont get tempted by package and outward appearances. We should love and respect our job.This company has invested 7 days time on you and you are fleeing away. Anyways you have already degrade your value in current organization by showing them your disinterest so better you should leave.
Now coming to your query for your relieving you can go through the clause of your employment letter and try to settle down the issue by talking to HR.One thing is clear HR is having a backup thats why she has agreed to relieve you on term it is because you are just 7 days old in system so she/he might be having some 2nd options shortlisted for same profile.
Another thing you can do is tyou can to talk to your future prospectus and clearly tell them that you had joined somewhere and now due to XYZ reason you want to join them but as its a short term employment you will not be able to produce any certificate.If they need you then they will be agree to have you then you can initiate the resign for one day notice and exit from system without paying anything.
First option is better and second option is what is followed by many persons now a days.Rest upto You.
Good Luck !!
28th October 2015 From India, Mohali
Thank you for your reply. My preference was to the second job always, but its just that their offer came very late. By the time, i had joined the company. So its unfortunate but not immature. Anyways, thanks for suggestions. I will try 1st one and if it does not work out then second.
28th October 2015 From India, Bengaluru