Is giving the worker one riyal in exchange for carrying the sacrificial animal to the car considered a bribe, especially since he requested it under the pretext of "tea money" and carrying it is not part of his duties?

Bribery is the means to achieve a need through artifice. Its origin is from the rope (risha’) used to reach water. The briber (rashi) is one who gives to someone who aids him in falsehood, and the recipient of the bribe (murtashi) is the taker, while the intermediary (ra'ish) is the one who mediates between them. However, what is given to obtain a right or repel an injustice is not considered bribery. Based on this, what was given to the worker is not a bribe; rather, it is compensation for his service of delivering the sheep, or it is a begging from him that was given to him, and its giver will be rewarded, Allah willing.