In this paper, we focus on interaction-preserving motion retargeting, which transfers human demonstrations to humanoids while maintaining spatial relationships with objects and terrain. Previous work, such as OmniRetarget, addresses this task through temporally coupled constrained optimization, requiring repeated sequential quadratic programming (SQP) iterations at each frame. We study this problem from an ordinary differential equation (ODE) perspective by modeling the continuous-time limit of its framewise Karush-Kuhn-Tucker (KKT) conditions as an ODE on the robot configuration manifold. This viewpoint offers two benefits: (i) it connects OmniRetarget's SQP iterations to a backward discretization of the ODE, enabling us to establish their local convergence under suitable regularity assumptions; and (ii) it leads to TaSP-KKT (tangent-space parametrization for KKT flow), a new retargeting method based on a forward discretization of the KKT flow. The proposed method achieves the same first-order convergence to the ODE solution as the corresponding backward scheme while requiring only one weighted tangent-cone projection and a closed-form manifold update per step, thereby avoiding repeated inner SQP iterations. Numerical experiments show that TaSP-KKT achieves retargeting quality comparable to, though slightly lower than, that of OmniRetarget while running approximately twice as fast.

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