Ultrasound computed tomography (USCT) is an emerging imaging modality that holds great promise for breast imaging. Full-waveform inversion (FWI)-based image reconstruction methods incorporate accurate wave physics to produce high spatial resolution quantitative images of speed of sound or other acoustic properties of breast tissues from USCT measurement data. However, FWI is computationally burdensome and requires a good initial guess of the speed of sound distribution due to the nonconvex nature of the underlying optimization problem (cycle-skipping). Alternatively, the use of a simplified linear model, such as the Born approximation, allows the image reconstruction problem to be formulated as a convex optimization problem, but sacrifices accuracy. This work proposes utilizing a convolutional neural network (CNN) to correct pressure data and accurately reconstruct images using a simplified forward model, thus combining the benefits of accurate reconstructions from traditional FWI methods with the reduced computational complexity of inversion with simplified models. Furthermore, applying this correction to the measurements before inversion avoids issues inherent to other deep learning reconstruction methods that first invert and then apply correction to the images. Specifically, correction in the measurement domain is well-defined by a mathematical model and avoids hallucinations by an improperly learned image prior. This reconstruction approach was validated with a set of anatomically realistic test images and compared to traditional reconstruction methods (FWI and uncorrected Born inversion), a data-driven learned reconstruction method, and a machine learning method for artifact correction in the image domain after reconstructing using an inaccurate physics model.