In general, the plugin does not retain the styling of table cells or borders, although it does retain formatting such as merged row and column cells, and heading and body rows. The rationale is that it is preferable for the table to conform to the styling conventions defined for the Moodle site. For example, I use the following CSS definitions to set the look of tables to have heading rows with white text on a blue background, every 2nd body row shaded, and borders on all cells.

table { margin-bottom:1.5em;box-shadow:0.8em 0.8em 0.8em 0.4em #888;table-layout:fixed}
table, td, th { border:1px solid blue}
tr { vertical-align:top;}
thead tr { background-color:blue;color:white;}
tbody > tr:nth-child(2n+1) {background-color:gray}

This requires that you have access to the theme design pages, and that the design permits the inclusion of custom CSS. I believe that modern themes support this (e.g. Essential, Adaptable).