Polarization-resolved chaotic emission intensities from a vertical-cavity surface-emitting laser (VCSEL) subject to feedback from a fiber Bragg grating (FBG) are numerically investigated. Time-delay (TD) signatures of the feedback are examined through various means including self-correlations of intensity time-series of individual polarizations, cross-correlation of intensities time-series between both polarizations, and permutation entropies calculated for the individual polarizations. The results show that the TD signatures can be clearly suppressed by selecting suitable operation parameters such as the feedback strength, FBG bandwidth, and Bragg frequency. Also, in the operational parameter space, numerical maps of TD signatures and effective bandwidths are obtained, which show regions of chaotic signals with both wide bandwidths and weak TD signatures. Finally, by comparing with a VCSEL subject to feedback from a mirror, the VCSEL subject to feedback from the FBG generally shows better concealment of the TD signatures with similar, or even wider, bandwidths.