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This article introduces an improved deep learning network, GRU-Net, designed to facilitate direct and precise phase unwrapping of wrapped phase measurements in gear tooth surface interferometry. GRU-Net incorporates a Gram matrix within each down-sampling process to compute style loss, thereby capturing essential stripe structure information features. This network exhibits enhanced capability in handling larger and more intricate gear tooth interferograms, particularly in scenarios involving pronounced noise and aliasing, while still yielding favorable outcomes. A comparative evaluation was conducted, contrasting GRU-Net with the Res-UNet network and other conventional methods. The results demonstrate that GRU-Net surpasses the alternative approaches in terms of unwrapping accuracy, noise resilience, and anti-aliasing capabilities, with accuracy improved by at least 24%, exhibiting significantly superior performance. Additionally, in contrast to the Res-UNet network, GRU-Net demonstrates accelerated learning speed and generates more compact models.