I seem to remember being told that 'tavolo' was a generic table and 'tavola' tended to be used for dining tables. Since mostly the table that has places at it is a dining table, 'tavola' seems most appropriate here.
a table with legs without the things for eating is a table (tavolo) A table 'dressed' for a meal becomes a tavola. The usual translation would be al tavolo or alla tavola. a tavola is at table or to table. The sentence is specific at the table. I translated it as al tavolo and was adjudged correct.
While the common idiom in English nowadays is to say 'at the table' saying that someone was 'at table' was actually used in the past. It appears to be the Italian idiom for this that it doesn't use the 'the'. Something to remember.