(I'm not a plumber) if the trap is not leaking and it is not open on the top part i feel I would not change it.
But maybe a clean would help.. that trap and (bottom) pipe seem to hold quite a bit of (dirty) water, and maybe sediment. Which can have it's own smell (and they don't have a trap upwords). I'd try some drain cleaner, maybe overnight, better according to instructions, and maybe flush it with loads of clean water afterwords, and see if the smell goes away for a good while. That could confirm (or dispell) that the smell is coming from that pipe.