Using the exact formula about the A-twisted correlation functions of two dimensional N=(2,2) gauged linear sigma model, we reconsidered the computation of the B-model Yukawa couplings of the local toric Calabi-Yau varieties. Our analysis is based on the exact result which has been evaluated from the supersymmetric localization technique and a careful treatment of its application. We provide a detailed description of a procedure to investigate the local B-model Yukawa couplings and also test our prescription by comparing the results with known expressions evaluated from the local mirror symmetry approach. Especially, we find that the ambiguities of classical intersection numbers of certain class of local toric Calabi-Yau varieties discovered before can be interpreted as degrees of freedom of the twisted mass deformations.