I had this same issue regarding the enfold theme. Unfortunately changing the border color did not work for me. For some reason the table is taking on a border color based on the color attribute rather than the border-color attribute. Unfortunately, changing this also changes the text that is inside the table column. I was able to get around this by adding the following code where I actually add a border with the background of my site to the table itself:
.tribe-events-tickets.tribe-events-tickets-rsvp {
border-color: #ffffff !important;
border-style: solid !important;
border-width: 3px !important;
}