Such is our world that the salary we get is based upon our previous salary and not as per our eligibility. I have seen guys getting much much more then what they deserve compared to what they should get. At the same time I have seen profiles getting rejected just because the current salary is way too low to be eligible for the profile though qualification and experience wise they are prefect for the job. Such is the world we live in. I cannot think that the company would have given you this salary if you would have told them your current salary. Such is the world we have chosen upon us to live in and such is the world we make it for us.
I dont say what you have done is correct but at times we dont have any choice. Anyways, from where I see, what you can do is keep your current job and take the offer letter to your HR and see if you can negotiate with them. They might not give you the same hike but you might get a decent raise. This will give you some peace of mind. Else, you can take some one in HR in confidence and seek their help.
Lastly, you can do is let the sleeping dogs lie and hope that they dont find it out but there is risk involved because as far as I know , IT companies do have a procedure of background check including verification of your educational documents as well as your experience and salary. How they do it depends from company to company. Any third party verification would be detailed where they would call on your HR number and ask for your details or it might be a simple call from your HR to the reference number you have given where they will just ask about your job details.
You can try to find out what sort of verification they do and based on that you can take your call. If possible try getting in touch with some current employee of the company to get the details.