Many countries in Irish (typically feminine ones that end with a slender letter) require an article.
An bhfuil tíortha le "an" i gcónaí baininscneach, agus gan "an" firinscneach?
Not necessarily; for example, Beinin is feminine, and an Congó is masculine.
Dúirt mo mhúinteoir gur athraigh "siad" cúpla tíortha agus anois tá gach ceann baininscneach. Cad a cheapann tú? D'athraigh siad An Congó le déanaí, dar leis.
The NEID entry for “Congo” shows that it still uses the article and remains unlenited in the nominative case, and the entry’s genitive examples show that it’s declined as an Chongó rather than na Congó, so that means that it’s still masculine. The tearma.ie entry for “Republic of the Congo” also shows Poblacht an Chongó (masculine) rather than Poblacht na Congó (feminine).
Did your teacher identify who “they” are?
If Pól would put things away when he is done using them, he wouldn't always have to ask where they are.