If they are laser cut, there is a pretty good chance they used nitrogen for the assist. This should not mess with the edges too much. If they used plasma, there is a real good chance they used air. Air assist edges have a certain amout of oxide, which can be tough to remove. The oxide will (of course) make the welding a lot harder. Probably a lot of crud in the weld, etc. If you have a few good close up pictures of the edge, I might be able to tell what process and gas was used.
If you want truly clean edges, you can use argon for assist, but it costs the earth. 99% of folks get by just fine with N2.
End of the day, you will have to clean up the edges with something if it is causing problems with the weld. File, grinder, carbide burr, router, there are a bunch of things that will work.