Yes, a grassy flavour with a light bitter note is typical for cold-pressed flaxseed oil, and it is described as characteristic of this product. It comes from the flaxseed itself and is expected in an unrefined oil. The taste can become more noticeable after the bottle has been opened because omega-3 fats are delicate and react to air and light.
This does not mean the oil is defective. However, as the oil ages or is stored poorly, it can oxidize and turn rancid. A rancid flaxseed oil usually smells sharp, sour, fishy or paint-like, and the taste becomes strongly unpleasant rather than just slightly bitter.
Before using an older bottle, check the smell first and then taste a tiny amount. If it seems clearly off, do not use it in food. To slow down oxidation, keep the bottle tightly closed in a cool, dark place — ideally in the refrigerator — and take it out only briefly when pouring.
If you are not used to the flavour, start with small portions mixed into cottage cheese, porridge or a smoothie, where the taste is less intense.