My initial reaction to the icon was that I could not recognize what the object was. I will explain why in a second, but my initial thought was that the character was a snail. This is because the yellow behind the gun nozzle blends in with the yellow/orange of the jacket at first glance.
Once I saw the gun I realized what it was supposed to be. I understand why your artist has put the yellow behind the nozzle of the gun and that is to make the nozzle stand out more on the blue background. But the yellow and its glow is conflicting (blending) with the yellow/orange on the main character visually.
Also you can loose the yellow glow on the right side of the character, you don’t need it because you already have a nice orange on the arm and collar/scarf which will go very nicely against the blue. For the white bits on the shoulder which would then be against the blue background, you could make the blue behind this area darker ever so slightly to make the white stand out more.
My second thought was, as a composition, the direction the gun is pointing draws your eye away from the character. If you angled the gun pointing upwards (mirrored on the horizontal) then your eye would be drawn to the character. (Don’t make the gun horizontal though.)
Next is the border… the white on the border makes the icon too ‘busy’ visually and could easily be kept plain. I think the focus should be kept on the character (which is your visual ‘brand’). You could make the border a dark color (not black) to separate it from the inner black and the central blue. It would also have to be slightly thinner if you did this. Or the easier way would be just to keep the white and put a thin black line around the edge of the icon, though you would have to test this. The blue central background looks great by the way.
The character can be centered ever so slightly (but not perfectly centered) as being right next to the border gives the character less definition (Keep the character on the left, just move it ever so slightly to the right). A bit of blue around the character on the left of the icon (around the characters right arm) would make the character ‘jump’ more visually. Make sure the nozzle of the gun does not touch the right hand side border though. It needs the blue around it.
I suppose this is a trick of the eye, but the barrel of the gun looks like it is curving slightly downwards. It probably is perfectly straight when you made it, it just looks curved downward slightly in comparison to the rest of the gun.
I would say to put a bit more red on the collar/scarf to separate the head from the body as the pink of the face, the orange on the scarf and the orange on the jacket all blend into each other.
Lastly, to make the nozzle of the gun to stand out from the blue background, remove the yellow behind it, and make part of the blue behind it a lighter blue as you did with the rays and streaks on the upper part of the blue background. Also the bottom of the guns ammo cartridge blends into the border. You could shorten the cartridge or put a bit of color between the border and the bottom of the cartridge to give more definition to the gun and make it stand out more visually.
Oh, and if you really wanted to keep the TD text then you could make it as a watermark effect on the upper right hand corner of the blue background ie. do your text in white, make it transparent, then place it on the blue central background.
A long analysis, but you did ask. I hope this helps 
