Learn French: Ils reçoivent une récompense pour leur travail.

In the verb recevoir (to receive), the letter c needs to keep its soft 's' sound. In French, a c followed by an o normally makes a hard 'k' sound. To keep the soft sound before the o in reçoivent, we add a cedilla to make it ç. You will also see this in the singular forms: je reçois, tu reçois, il/elle reçoit.

The infinitive is recevoir, but here it is spelled with 'reçoi-'. Does the stem always change like this?

No, recevoir is an irregular verb with a 'boot' pattern in the present tense. The stem changes to reçoi- for the singular forms (je, tu, il) and the third-person plural (ils/elles). However, for nous and vous, it keeps the original stem without the 'i' and without the cedilla: nous recevons, vous recevez.

Why is it leur travail and not leurs travail since the subject ils (they) is plural?

The possessive adjective leur (their) must match the thing being owned, not the owners. Even though 'they' are plural, the word travail (work) is singular here, so you use the singular leur. If they were receiving an award for multiple tasks, it would be leurs travaux.