Refined or processed grains can have added sugars and typically made from white flour which can increase triglycerides. You need to avoid enriched or bleached white bread, wheat bread, or pasta as well as sugary cereals, instant rice, bagels, pizza, pastries, pies, cookies, and cakes.
Whole grains that are natural will avoid these issues due to fiber/carb balance and which is why people are pushed over to whole grains. However this is half the story.
If you are eating Ezekial bread or having whole wheat bread then with the rest of your diet/exercise you can still lower Tris no problem
Some healthy touted whole grain products can have very high amounts of net carbs. If you eat that in large quantities then there is no benefit of that whole grain as it will raise Tris.
If you having whole grain wheat bread with a sandwich then it has a good balance.
For example look at Quaker Oats. Often touted as great breakfast food and often people have a cup of this stuff:
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Advertised as 100% Whole Grain. But you are eating 46 grams of carbs in one sitting (protein and fat are decent for a grain though).
So only has 2 grams of sugars but still a carb bomb that accumulates into raised triglycerides.
Whole grain pastas are another bomb....usually end up with 40-60 grams of carbs per normal serving.
Now we get into quantity. If you have whole grain pasta 1x a week then no real effect. Better than refined wheat pastas for sure and doubt people eat that nightly.
But we used to see so many recommendations to have a big bowl of oatmeal/oats daily but there was little account taken for the blood sugar spikes and accumulation of empty carbs.
The reason I say this is elevated carbs be it refined OR Whole Grain will still raise Tris:
Evidence from a statement released by the National Heart, Lung and Blood Institute, panel on Detection, Evaluation, and treatment of High Blood Cholesterol in Adults (ATP III), suggests that very high intakes of carbohydrates (CHO) (greater than 60 percent of total calories) are accompanied by a rise in triglycerides. The recommendation by ATP III regarding dietary “Carbohydrate intakes should be limited to 60 percent of total calories. Lower intakes (e.g., 50 percent of calories) should be considered for persons with metabolic syndrome who have elevated triglycerides or low HDL cholesterol (the good cholesterol).
Typical U.S. diet could easily surpass 50-60% of calories, even those eating whole grains. (Oatmeal, pizza, pasta, cookies).
The real culprit is the marketing campaign of "Whole Grains" slapped on products all over (Just like "Fat Free" in the 90s and now "Gluten Free").
But look at Ezekiel:
2 slices is 30 - 6 = 24 net carbs. Not bad if you have 2 slices for breakfast or for a sandwich at lunch. So quantity is fine. But you have two of these with breakfast, a plate of whole grain pasta at lunch and then a carby dinner....Tris will accumulate.