No. You can give something you own away. You obviously don’t own it anymore after you gave it away. Being able to give what you own away is part of ownership. (You can’t give something away you don’t own.)
Since you can still make a local copy of your clickstream data (every browser has some sort of history function) you don’t even really give it away, you keep it and hand over a copy (maybe not technically but it is still the exact same data) to Bing.
Here is an analogy: Imagine a scale which, after you agreed to it, automatically sends your weight to the manufacturer every time you use it. The manufacturer made it clear when you agreed that you will not be able to access your weight history. While slightly creepy, I don’t see any ethical or legal problems with that. You own the weight displayed on the scale, you can therefore also agree to send this weight to whomever you want, even if they don’t let you access your weight history. You are also free to make your own local copy of your weight history (for example by writing you weight on a piece of paper every time you use the scale).
Since you can still make a local copy of your clickstream data (every browser has some sort of history function) you don’t even really give it away, you keep it and hand over a copy (maybe not technically but it is still the exact same data) to Bing.
Here is an analogy: Imagine a scale which, after you agreed to it, automatically sends your weight to the manufacturer every time you use it. The manufacturer made it clear when you agreed that you will not be able to access your weight history. While slightly creepy, I don’t see any ethical or legal problems with that. You own the weight displayed on the scale, you can therefore also agree to send this weight to whomever you want, even if they don’t let you access your weight history. You are also free to make your own local copy of your weight history (for example by writing you weight on a piece of paper every time you use the scale).