Put something underneath it, or cordon it off somehow. This prevents them from walking close enough to hit their head in the first place.
You can plant some shrubs or flowers underneath it; make sure to get appropriate sun / shade tolerant plants. You could put a little sculpture, or just landscape it with mulch. People tend to avoid walking on mulch, even if there's nothing planted.
The other option is to put some kind of barrier around it. A small fence, some large rocks / boulders, etc.
Edited after your edit: Make the BBQ slightly bigger than the overhang, or stick out further than the overhang. Supplement with plants or other ideas from my answer if needed. This prevents people from being able to walk where they would hit their head in the first place, negating the need for any foam or other material on the overhang itself.