It's the front F key.
It probably fell off because the rod unscrewed itself. Probably nothing to do with a bump.
The saxophone will play perfectly without it.
Earlier horns didn't have it and some players remove it to save fudging it and squeaking.
Put it somewhere safe and the next time your horn is in for maintenance it can be refitted. Did you find the screw/rod? Keep that safe too, if you have it.
So, now we know what fell off and it has nothing to do with tuning, grease up the cork and push the mouthpiece further in.