General Electric Co., which partnered with the now-bankrupt invention startup Quirky Inc. to create smart-home products, says the startup’s failure greatly hurt GE’s reputation.

Quirky, which was founded in 2009 and filed for chapter 11 protection this year, has “already caused substantial damage to the reputation of GE and to its trademark,” GE said in bankruptcy-court documents, as Quirky failed to keep up customer service support on the products that the companies partnered to create, it said. GE says that as a result it...