Hi,
Strangely enough, this same part is broken on mine. Previous owner had used double sided tape, but I just am too lazy to bother re affixing it properly.
The 3 hooks are made of plastic and they fail where the hooks lose their elasticity so they no longer firmly grip - in some cases hook(s) may break away completely.
A piece of decent double sided tape is the cheapest solution as from what I have heard is that they are expensive for what they are from the dealership. I once tried getting a set from the breakers but the hooks failed upon removal. I guess the hooks take the brunt of the forces applied every time the compartment is opened.
Glue it back on. I had this on one car and it was still firmly attached later after four years of family use. Unlike the original fixings from factory which break anyway
A new piece of trim will be expensive and probably not match the original faded wood on the other side.