This appears to be a form of symbiotic relationship as both parties are benefitting from the relationship. The herbivore is losing parasites and the bird is gaining food. To test whether it is obligate or facultative you would set up a group observe whether the bird has another food source - if it does then the relationship is facultative. If the bird only feeds on the ticks form the herbivore then it is an obligate relationship. If you can somehow exclude the bird from removing the tick from the herbivore, you can test whether a) the parasite will impede the herbivore's lifestyle significantly b) whether something else will remove the tick.