All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the situation is as you mentioned in the question that the marriage registrar had written the amount of the dowry in your presence and you signed it as usual, then this is considered as consent on your part about this written amount and it is the mentioned dowry that the wife deserves.
However, the dowry is the sole right of the wife and she has the right to ask for it or to renounce all or part of it if she is adult and sane. Therefore, you may agree with your wife about this matter, and if she wishes, she may renounce this dowry or part of it.
In case your wife renounces this dowry or part of it and you fear that her family will object, then she may use Tawriyah (i.e. saying something which has more than one meaning and intending a meaning different from what the listener is likely to understand) from which they may understand that she has received the money from you.
Indeed, Tawriyah may be used instead of lying. For more benefit, please refer to Fataawa 84728 and 88412.
Allaah Knows best.