To determine how many ounces of cookies will be left over after putting them into 4-ounce bags, we can perform the division of the total ounces of cookies by the size of each bag.
- Divide the total amount of cookies (1,441 ounces) by the size of each bag (4 ounces):
\[ \frac{1441}{4} \]
- Performing the division, we find:
\[ 1441 \div 4 = 360 \text{ R } 1 \]
This means that when 1,441 is divided by 4, 360 full bags can be filled, and there will be a remainder of 1 ounce.
Thus, the number of ounces of cookies left over after filling as many bags as possible is:
\[ \boxed{1} \]