What is a tech pack and does a lingerie factory need one?

A tech pack is the document that tells a factory how to make one style: flat sketches and construction details, a measurement table with grading rules, a bill of materials, seam and stitch instructions, labelling, packing and the acceptance standard.

Without one, a factory does not quote your product, it quotes its guess at your product. That guess is where the price gap between two quotes usually comes from, and where the first sample goes wrong.