To add, I would also say that Tuco's grill represents the change that Hank refuses to go through. Hence, why he throws it, and for that matter, El Paso in the river. Heisenberg calls him and (if I'm not getting into spoiler territory), by extension death calls for him. So in a small way, I come to see Tuco's grill as both a grizzly reminder not only to the violence inflicted upon Hank, but the violence that he has inflicted on others.
Maybe the grill represents the tainted idea of being rewarded? I mean, Hank killed Tuco and yet, instead of having cuffs slapped on his wrists, people clap their hands on his back. "Good job, Hank", "Way to get that bastard!". But at the end of the day, Hank took a life, and I think that haunts him throughout the series. He constantly fears his own fate, verbally and emotionally (its why he has anxiety/panic attacks?) because he regrets his own thirst and actions for and towards violence.