As mark mentioned there should be a metal elbow going into the cap with a nut for adjusting. I had this issue with my 75 DT250. I believe years 74-76 DT250,360 and 400 use the same cables but don't quote me. The new cables that you see available aren't quite right. The lengths are off and their missing the metal elbow.
I had to fabricate my own metal tube by cutting, bending and flaring the end that goes into the cap using just a piece of tubing i had bought. Its still not quite right and i cant use the injection either because i cant get the pump and carb in sync the way i need them to be.
Dave at KDI needs a NOS or super good condition complete cable set for these 3 years so he can begin the process of having these made and if you don't know already his stuff is spot on! I been trying to track a set down.

On another note be careful where you feed your throttle cable. Because the lengths are off on all 3 cables i discovered that the splitter tube did not like to stay in the holder clip. It would slip out and cause the bike to rev up if i turned too sharp. Had to do a little zip tying to keep everything in place.

Slack is at the Pump cable. Ones the carb cable pulls and snaps back a small slack is left at the pump cable. If this will not cause any issue I will leave as it is . A slight open at the pump should not cause any issues. Any thoughts.

The pump pulley and body will each have a mark and these must line up with each other. I can't remember on that model if the alignment is with throttle closed or fully open, but it will be obvious when you look at the oil pump and move the twist grip.

Having slack at the oil pump cable will likely mean engine doesn't get enough oil.

Will replacing the spring at the Pump solve this problem? I lined up the pin at throttle closed. It does not close all the way when carb cable return to close position. This will still keep oil pump in slight open position. hence oil will be flowing

Try a bit of oil on the Pulley pivot . I had the same problem with an RD 400 that had sat for about 30 years .
Once lubed up , it would close off properly .