Wiring under cabinet lights

We are replacing our under cabinet lights. The first photo shows the wiring that remains after removing one of the old lights. The new lights come with the strain relief fitting shown in the second photo.

Is it proper to simply put the wires through the strain relief "as is" and clamp it down, or should I be doing something more like wrapping the wires in something first? I'm not very knowledgeable on wiring standards and don't want to do something dumb.

I'm not an elctriction but I'm sure that the splice needs to be within an approved sealed junction box & no romex should be left exposed.

The romex needs to have a connector see here for options (note that the twin screw clamp type appears to be shown installed backwards. It's to be installed from the outside of the box with the nut on the inside of the box).

Without seeing this first hand, the following is a suggestion & MAY not be the best approach to this task.

It's a BEST guess recommendation......

If I were doing this, I would use an extra low profile j-box with a single metal (twin screw clamp type) for both romex cables.

I would run the two cables through the connector & clamp the connector to the cables so ultimately the connector will be behind the wall or between the wall & the wood back (may have to remove a bit more wood for clearance).

Then remove the middle knockout of one side of the box.

Drill two holes on the that side for the mounting screws.

Lay out holes so the screws will have sufficient wood to grab. Don't want the screws too close to the edge. Don't put the holes in knockouts. The screws will be installed with a slight uphill trajectory due to the driver hitting the box's opposite side so keep that in mind.

Install the connector/romex (tighten locknut).

Install box against wood back so opening is pointing down.

Attach box to wood using screws long enough to allow full penitration into wood but not so long as to interfere with romex behind the wall.

The new light(s) cable will then be run to the j-box.

Happy wiring

P.S. Keep the smoke in the wires & you'll be fine.