Recruitment - Agency claim - Mr Y directly approached the firm for the said vacant position

Dear Experts - I request your views on the following:

It is the practice of recruiting officials in higher-level through recruitment Agency in Corporate Companies. As such the Agency has referred persons X, Y, Z, and so on. Mr X was recruited after the interview and the Agency was paid a fee for such recruitment. However, after two years Mr X left the employment. Knowing the said vacancy caused due to Mr X's resignation, Mr Y directly approached the firm for the said vacant position. After the interview, the Y got selected and appointed in the said firm and is working for the past 1.5 years. Now the Recruitment Agency claims that since the Candidate "Y" also referred by the agency, the said firm is liable to pay the recruitment process fee to the recruitment agency. Now my query is whether the recruitment Agency has the right to make such claim against the for the said recruitment of "Y", although the recruitment was made directly now.

Dear Sridharan,
This is a matter between a purchaser and a service provider. Before providing with the services, has the recruitment company (service provider) signed any contract with the company (purchaser)? If yes then please provide the terms and conditions of the contract.
Especially, check the clause on the "lock-in of the candidates" as well as "validity period" of the contract. "Lock-in of the candidates" means a recruitment company will recommend a certain number of candidates to the company. Since the date of recommendation, the candidature of the candidates gets locked and for each recruitment amongst the recommended lot, the company (purchaser) is required to pay a certain fee to the recruitment company. This lock-in period will remain valid for the _____ years since the date of recommendation.
If the contract is not clearly worded, it raises the confusion and both sides start interpreting the terms of the contract to their advantage.
Thanks,
Dinesh Divekar