I don't believe the DX laser has an IR filter. Only higher priced and some higher power lasers have them. If it does not state it has one on the site, it doesn't.
As far as adding one, you would have to glue/clamp ?, one in front of the aperture.
It would diminish the power of the 532nm (green), but if you bought a high quality IR filter, not by much.
BTW: unless you are holding this laser right next to your head, it's not that big of a deal.(on a 50mW)