I have strained but do not anymore. Too much trouble versus the benefit.
If asking about the skin on the pods…Sometimes, but not that often, I will try to slip the peels from the pods after softening up in a pot with broth. Also labor intensiver depedning non the pods used. Usually I just blend the bejeezus out of the pods with the . Finished product it is hard to tell the peels are there.
Most often I break up the pod into pieces as place in the pot. And depending on what I want that day I toss out the seeds or many of them before tossing pods into the pot with chicken or beef stock to simmer and soften. Then in batches toss into blender till full smooth, and toss that into pot. I often make pretty massive batches of this sauce, and freeze some of the surplus to later turn into enchilada sauce, or taco meat seasoning, or good ole texas red chili as you did.
I brown meat cut i to cubes, then toss the sauce, unseasoned, in with the meat and then season to taste with salt, oregano, garlic, diced onion, etc. very late in the cook I may add some ground cumin and do add some masa, oremixed with a bit of the sauce to avoid lumps. That last step really puts it over the top flavorwise for me.