Wow! First, you got a job, then you found a better option, and now you want to switch in just a week. Moreover, you concealed the fact about your current employment. You are not the only person who thinks the world is full of such immature decision-makers. You need to analyze why you want to change jobs after only 7 days of working. If a similar situation arises in your new company, will you search for another one? How many jobs will you hop like this?
Think and decide sincerely. Don't get tempted by the package and outward appearances. We should love and respect our job. This company has invested 7 days' time in you, and you are fleeing away. Anyways, you have already degraded your value in the current organization by showing them your disinterest, so it would be better if you leave.
Relieving Process and HR Communication
Now, coming to your query about your relieving, you can go through the clause of your employment letter and try to settle the issue by talking to HR. One thing is clear: HR has a backup, which is why they have agreed to relieve you on terms. It's because you are just 7 days old in the system, so they might have some second options shortlisted for the same profile.
Another thing you can do is to talk to your future prospects and clearly explain that you had joined somewhere and now, due to XYZ reason, you want to join them. However, as it's a short-term employment, you will not be able to provide any certificates. If they need you, they will agree to have you, and then you can initiate the resignation with a one-day notice and exit from the system without paying anything.
The first option is better, and the second option is what many people are following nowadays. The choice is up to you.
Good Luck!