"They do not offer food."
Translation:De bjuder inte på mat.
Zmrzlina is right in that Bjuda = to offer something for free and Erbjuda = to offer something at a price. But I think the English word Offer can have both of these meanings. As in: Can I offer you a drink v.s. I can offer this xxx at a special price. . . . but then again, - we are not here to learn English!
I'd say it is not a particle verb, it's just a verb which requires a preposition in order to have a second object. The only object it can take without a preposition is the person invited, or "treated", but if you want to say what you treat them to, you need a preposition. Much like in English with I treated them to food.