How Should I Handle Termination Without Hurting an Employee's Future Career?

So, I have a very new company with fewer than 5 employees. One of our senior employees helped me make the job offer letter. After opening the company for the first time, I had to terminate someone due to very poor performance. However, I do not want that to reflect on their career; hence, I told them that, due to COVID, I had to let them go. I will write the same on the relieving letter as well. According to me, the termination clause in the offer letter states a minimum notice, so I gave them 30 days' salary without any work. This employee is threatening me to provide a 60-day salary due to the last sentence in the probation period. What is the correct thing to do here?

Probationary period

As per the organization's policy, the probation period applicable to you shall be six (6) months. During probation, the company reserves the right to terminate the employment without any notice if your performance is not deemed satisfactory. After the probation period, the notice period will be two months.

Termination

The company may terminate your employment at any time for cause. After the end of your probationary period, the company may terminate your employment without cause at any time by providing you with the minimum notice, or pay in lieu of such notice, and any severance pay required by the then-effective Employment Standards Act.

A caveat first, we are familiar with Indian laws and cannot speak with authority on Canadian laws. Yet, based on general principles, it is suggested as follows:

You have mentioned a notice period of one month, but there is no mention of it in the extracted termination clause; it only states the minimum notice. In that case, the notice period in the probation clause is enforceable. The mention of a minimum notice period there cannot reduce that liability.