You could quickly get the table and this kind of customizations using the following editor: https://www.latex-tables.com; on the right of the page you can set the border colour.
Or try setting the color for each box, adapting a script like this:
\documentclass[12pt,a4paper]{book} \usepackage{colortbl} \usepackage{hhline} \begin{document} \begin{table} \centering \refstepcounter{table} \label{t:test} \arrayrulecolor[rgb]{0.753,0.753,0.753} \begin{tabular}{llll} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \\ \hhline{->{\arrayrulecolor{white}}->{\arrayrulecolor[rgb]{0.753,0.753,0.753}}->{\arrayrulecolor{white}}-} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \\ \hhline{>{\arrayrulecolor[rgb]{0.753,0.753,0.753}}->{\arrayrulecolor{white}}->{\arrayrulecolor[rgb]{0.753,0.753,0.753}}->{\arrayrulecolor{white}}-} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \\ \hhline{>{\arrayrulecolor[rgb]{0.753,0.753,0.753}}->{\arrayrulecolor{white}}->{\arrayrulecolor[rgb]{0.753,0.753,0.753}}->{\arrayrulecolor{white}}-} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \\ \hhline{>{\arrayrulecolor[rgb]{0.753,0.753,0.753}}->{\arrayrulecolor{white}}->{\arrayrulecolor[rgb]{0.753,0.753,0.753}}->{\arrayrulecolor{white}}-} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \\ \hhline{>{\arrayrulecolor[rgb]{0.753,0.753,0.753}}->{\arrayrulecolor{white}}->{\arrayrulecolor[rgb]{0.753,0.753,0.753}}->{\arrayrulecolor{white}}-} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \end{tabular} \arrayrulecolor{black} \end{table} % or black-white hhline: \begin{table} \centering \refstepcounter{table} \label{} \arrayrulecolor{black} \begin{tabular}{llll} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \\ \hhline{->{\arrayrulecolor{white}}->{\arrayrulecolor{black}}->{\arrayrulecolor{white}}-} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \\ \hhline{>{\arrayrulecolor{black}}->{\arrayrulecolor{white}}->{\arrayrulecolor{black}}->{\arrayrulecolor{white}}-} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \\ \hhline{>{\arrayrulecolor{black}}->{\arrayrulecolor{white}}->{\arrayrulecolor{black}}->{\arrayrulecolor{white}}-} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \\ \hhline{>{\arrayrulecolor{black}}->{\arrayrulecolor{white}}->{\arrayrulecolor{black}}->{\arrayrulecolor{white}}-} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \\ \hhline{>{\arrayrulecolor{black}}->{\arrayrulecolor{white}}->{\arrayrulecolor{black}}->{\arrayrulecolor{white}}-} t & {\cellcolor[rgb]{0.753,0.753,0.753}}e & s & {\cellcolor[rgb]{0.753,0.753,0.753}}t \end{tabular} \arrayrulecolor{black} \end{table} \end{document}