When hiking in the mountains my VO2 value drops because I hike slower up the mountain. Garmin does not correct for the meters elevation. It would be great if this comes in the system.

The VO₂max estimates during walking are highly approximative, because the conditions vary wildly  - it is not only the grade of hill climbs, but also the terrain, the weather, gear & wear, carried weight, and other aspects that cannot be measured by any sensors.

You will get more accurate results only from running (preferably with a HRM chest strap) or from cycling with a powermeter. The climb & descent grade is already taken in account - see the description of the Firstbeat method that Garmin uses in their article at Firstbeat Analytics

Hiking doesn't calculate VO2 max values. Are you logging the hike as walking or hiking? 

The VO₂max could be still coming from the all-day HR estimate, which is even less accurate than from walking. It is principally based only on the body parameters (age, gender, weight,..), and the Resting and Max HR values. Even more useless than the walking estimate.

I am logging in with walking. And it does effect the vo2 max. Because I see it drop after a mountain hike and rise when I doe a flat hike

So, use the hiking activity instead for hiking, it doesn't record any VO2max.