which word should I use to describe it?

I don't think there is a term for that in English, at least I have never heard anything in the US to describe this. This might be because it is extremely rare for us to have loose tea leaves in our tea. Most of us use tea bags, and a few of us use either tea balls or strainers.

I might describe this as "straining" the tea leaves with the teacup cover. For that matter, teacups over here don't have covers.

There is no word in British English either.

The closest expression would be "straining" here too, that is, using a perforated object to catch the leaves and let the liquid through.

A tea strainer, in fact.

(imho pushing the leaves to one side with a cover or a spoon/spatula would not work very well!)

Probably there is no word because tea-drinking is not as much a part of the culture of English-speakers as it is of people in China. Except, of course, for some few deluded types in Angle-land . . .

Drinking tea in a Chinese restaurant will result in "leaves in mouth," unless they use tea bags.

Thank you all very much!

oolongteasup?