Assuming the quote is accurate, I found this to be somewhat amusing. It evoked some funny imagery. The teiva was surrounded by torrential rains and flooding and someone on Noah's ark is going to open an umbrella to stay dry. 

So, what did he mean?

Is wearing a mask an exercise in futility in the beis medrash the way opening an umbrella on the deck of the Ark is an exercise in futility because there is so much COVID in the beis medrash?

The survival of the people on the Ark was based on their faith in God's protection, and opening an umbrella would be countering that faith. Survival in the beis medrash in today's times is also base don faith, and wearing a mask would be opposing that and exhibiting lack of faith.

Rav Kotler's statement also reminded me of the statement of a rav a bunch of years ago that compared the beis medrash with Noah's Ark, saying that the yeshiva world today is like Noah's Ark, protecting us from all the external negative influences.

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Whatever it is exactly that he meant, I found the comparison to be evocative.