PetSmart Inc. offered to amend its debt documents, providing further protection for senior lenders as it seeks to quell concerns over an asset transfer that put some parts of the pet-supply retailer beyond creditors’ reach.

The closely held pet superstore offered March 25 to tighten its credit agreement if existing lenders drop ongoing litigation, according to people with knowledge of the matter. PetSmart is offering to limit its ability to layer on additional senior debt, and is providing additional incentives including consent fees, said the people. To pass the amendment, the retailer needs approval from lenders holding more than 50...