The DT125RE/DT125X doesn't have the reedswitch restriction that the '00-'03 models had.
The exhaust has the same restriction as the '00-'03 models, and it is also fitted with a catalytic converter.
The catalytic converter is removable but there would be a hole in the exhaust where a pipe to the airbox goes.
The pipe to the airbox would need removing and the hole left over would need to be blocked off.
I don't know if it would be compulsory to have the catalytic converter fitted for the MOT but I'm sure you'll find out on web forums in 2007 when the DT125RE/DT125X will be due for their first MOT. My advice would be to either get a DEP exhaust, or get a second-hand exhaust from a '88-'99 model bike and de-restrict that. The second-hand exhaust will fit but one bracket needs moving slightly, and the silencer will need a rubber sleeve fitting over the joint with the front pipe as the pipes are a slightly different diameter (size). To join pipes in the past on my old DT50MX I used to use a piece of an old bicycle inner-tube with a couple of cable-ties.

The inlet manifold is restricted in the same way as the '00-'03 models:

Modify Inlet Manifold

First you need to remove the carburettor (refer to Haynes Manual). To remove the inlet manifold, unscrew the 4 x 10MM bolts and gently remove the two-stroke oil feed pipe attached to the top of it. And either block the oil feed pipe with something small or just make sure it stays up in the air so no oil leaks out of it. You should now be able to remove the inlet manifold, although it may require a little help to un-stick the manifold gasket from the engine.

The square rubber piece attached to the inlet manifold (as shown in the photo) is designed to channel all the air/fuel mixture to the tip of the reed valve block, restricting the flow. To remove this square piece, get a stanley knife and first cut it off flat with the base. Next you need to carefully trim the flat surface so that you get a nice curved surface from the hole to the outside.

 

When i refitted mine, i used instant gasket paste to ensure a good seal on re-assembly.

Also: When re-assembling, block the hole in the large air bottle (the one that's got a screw holding it to the frame). This is another item that's been fitted to newer DTR's to mess with the air flow. Ideally it would be better to find an older model inlet pipe to replace the one (with the large hole in the left hand side) that's fitted between the airbox and the carburettor. To block the air bottle hole on mine i've used duct tape over the hole (on the bottle)(because duct tape is strong) and refitted the bottle hence blocking the hole. It seemed to have worked.
Make sure the bottle seals in the hole properly with the duct tape on it. I put a square of duct tape over the hole with a strip all the way round the edge to hold it in place.

And lastly on the inlet restrictions, remove the rubber snorkel off the top of the airbox under the seat. It'll help the air flow and you'll hear the induction sound.

Please note:

If you are planning to do a lot of muddy, wet greenlaning/offroading then it would probably be best to leave the rubber snorkel on as it would stop the airbox from sucking loads of crap into it.

The NEW restriction that is used on these bikes is a simple one to fix:

Going into the speedo is a four pin connecting block. There are 4 wires going into the block and only 3 wires coming out the speedo side. Just find the Green/Black wire going into the block, clip it to separate it from the block, and strip the end and join a small piece of wire to it (long enough to to join to an earth on the frame). When the Green/Black wire is earthed to the frame this stops the YPVS from retarding over 7000 RPM. The engine should rev freely now.

If it still doesn't then take the front pipe off and check that the Powervalve is fitted the correct way round as described in the de-restricting section for the '97-'99 models.