Difficult to say without more information.
The "telephone experience" may either be the key criteria or the rest of your CV meets requirements and the "decision maker" simply needs the information to complete the vetting to advance you to the next round. However, " . . . should have at least two years telephone call centre experience . . ." suggests they might expect this to be fairly recent or within your current position. If they are asking for the name of a Company then it would suggest it is more likely that checks/references are taken up. I do not think it would be a good idea to falsify/fudge the data.
Why not take the initiative and tell the truth that you cannot remember in detail but if you can elaborate upon other roles which did involve customer service/sales especially using the telephone, that may help.
Specific examples of positive outcomes should be included. Although not necessarily on the 'phone, can you provide examples within other areas where your "attention to detail" can be demonstrated/evidenced?
I think the Company would be more impressed with your honesty rather than run the risk of being found out as deceitful. It will play on your mind too, if you actually get the job. Don't forget you may be working a probationary period and there would still be time to terminate your employment. That won't look good on your cv.
If the next stage is an interview, then that is your ideal opportunity to enhance your skills and experience further. You can also include that you have identified an area for development - to develop/refine your telephone skills to meet/exceed standards expected of the job.
If you make the call, don't forget that how you conduct yourself may also affect the outcome. A positive reinforcement of your skills/personality may encourage them to progress your application further, even though you cannot provide evidence of one area of your work history.