This paper addresses the optimization problem of symbol-level precoding (SLP) in the downlink of a multiuser multiple-input multiple-output (MU-MIMO) wireless system while the precoder's output is subject to partially-known distortions. In particular, we assume a linear distortion model with bounded additive noise. The original signal-to-interference-plus-noise ratio (SINR) -constrained SLP problem minimizing the total transmit power is first reformulated as a penalized unconstrained problem, which is referred to as the relaxed robust formulation. We then adopt a worst-case design approach to protect the users' intended symbols and the targeted constructive interference with a desired level of confidence. Due to the non-convexity of the relaxed robust formulation, we propose an iterative algorithm based on the block coordinate ascent-descent method. We show through simulation results that the proposed robust design is flexible in the sense that the CI constraints can be relaxed so as to keep a desirable balance between achievable rate and power consumption. Remarkably, the new formulation yields more energy-efficient solutions for appropriate choices of the penalty parameter, compared to the original problem.