I'm Doug, and I'm sorry to hear of the confusion. My goal is to provide you with excellent service today. Thanks for asking for me.
Under CA law, in order for your unemployment to be decreased because of a work pension you earn, 4 separate facts must exist.
1. The pension relates to prior employment
2. Wages earned from the employer paying the pension are included in your present claim's base period (which in your case is not possible as you have not worked for Company T in 7 years)
3. The pension plan is funded solely by your employer (meaning that you did not contribute to the pension).
So, even if all criteria but this one is met, if you paid into the pension fund---think a 401K where you paid part and your employer paid part----you still would be able to get a full unemployment claim paid. Only pensions that are 100% paid for by the employer are subject to being set off against your unemployment.
4. The time spent working for the pension employer increased the value of the pension or counted toward vesting of the pension.
Under the circumstances, there is no need for you to check on whether you paid into the pension with some of your own funds as none of the wages you earned in the base period for this unemployment claim came from the employer responsible for your pension.
You are good to go. You may collect full unemployment benefits as well as your pension from company T.
You may reply back to me using the Reply link and I will be happy to continue to assist you until I am able to address your concerns, to your satisfaction.
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I wish you and yours the best in 2015,