I think you are using a modified besocial theme and those are the tables inside of posts.
Find your index_besocial.css file and change the following:
/* Styling for tables inside posts */
.inner > .bbc_table_container > .bbc_table td,
.messageContent > .bbc_table_container > .bbc_table td {
border-bottom: 1px solid #ccc;
border-right: 1px solid #ccc;
}
.inner > .bbc_table_container > .bbc_table th,
.messageContent > .bbc_table_container > .bbc_table th {
border-bottom: 1px solid #bbb;
border-right: 1px solid #ccc;
}
and change those to none
/* Styling for tables inside posts */
.inner > .bbc_table_container > .bbc_table td,
.messageContent > .bbc_table_container > .bbc_table td {
border-bottom: none;
border-right: none;
}
.inner > .bbc_table_container > .bbc_table th,
.messageContent > .bbc_table_container > .bbc_table th {
border-bottom: none;
border-right: none;
}
or just put the above in a custom.css file and leave the other file alone.