Remove duck neck and giblets.
Reserve duck neck for other uses; rinse giblets and set aside.
Cut duck into serving-size pieces; pull off and discard lumps of fat.
Rinse duck pieces; pat dry.
Place all duck pieces (including giblets) in a 12-to 14-inch frying pan over medium-low heat.
Cook, uncovered, turning pieces as needed, until well browned, about 45 minutes.
Remove duck from pan and set aside.
Pour off and discard all but 1/4 cup of the drippings.
To drippings in pan, add onion and garlic; cook, stirring, until onion is soft.
Add tomato sauce, water, and all olives; stir well.
Return duck to pan, reduce heat to low, cover, and simmer until meat is tender when pierced, about 1 hour.
Skim and discard fat; season to taste with salt.