Yes. That piece was designed to allow the handle to work only when the window is in the down position. It can be eliminated. I seen it in place in the first 2 pictures you sent me. What made you take it out? That piece has been discontinued for over 20 years. If you can get it back in plce that spring holds it in place just like in the picture you sent me.
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It slides down when the sash hits it and allows the handle to operate. I know you can do away with it. It basically just sits in place and the spring holds it there. I don't have a mechanism in front of me at the moment. That bottom nylon holder can be duplicated with 2 heavy wire ties run thru the bracket. Again oil and grease these pieces lightly so the slide easily.
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The area on the left leg lower section appears to be bent a bit. If it is straighten it. Lube it and reinstall it as you have it pictured. Good Luck. I hope that helps. Maybe even mess with the latch and discover how that rod activates the handle.
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That plastic coated L piece can be adjusted to the left more so it supports the rod better. Give some of these tips a try and report back. Good Luck.