It is not essential to form a specific intention for Tawaf or Sa`i or any of the rituals of Hajj; rather the general intention is sufficient, namely the intention to perform Hajj or `Umrah when entering Ihram. Based on that, your Tawaf was valid and you do not have to do anything else.

Based on that: If you entered ihram for ‘umrah and had formed the intention to do the rituals after crossing this distance, and the like, then there is no blame on you, in sha Allah, and your ‘umrah is valid. It does not seem that you have to do anything.