Apple pomace is a by-product of the apple processing industry and can be used for various uses such as animal feed, for composting, or to extract valuable compounds such as pectin or antioxidants. In recent years, it has also gained attention as a potential food ingredient due to its fibre content and antioxidant properties. The aim of this study was to examine the effect of three parameters: the percentage of wheat flour replaced by extrudate (5%, 10%, and 15%), the percentage of apple pomace in the extrudate (15%, 30%, and 45% based on the mass of corn grits), and the particle size of the extrudate (<250 µm; 250–1000 µm; 1000–2000 µm) on the properties of cookies, using the Box–Behnken experimental design. The addition of extrudates enriched with apple pomace significantly increased the total fibre and ash content of the cookies. The hydroxymethylfurfural content also increased, but not above the permitted limits (25 mg/kg). The sensory quality was strongly influenced by the particle size, especially the hardness, graininess, and appearance of the cookies. The addition of extrudate led to a darker colour of the cookies and a significant increase in the proportion of red tones, but generally had no negative influence on the acceptability of the cookies and their microbiological stability during the 6-month storage period.