What do you do when you catch yourself feeling sad about things/people that do not matter anymore?

I distract myself with something/someone else

Listening to music, and/or distract myself with activities. If around here, ask and reply on a lot of questions. Shout out loud. If none of it works out well, I'll resent to a foul mood, eventually a numb one.

Realize that they do matter still, and try to figure out why.

I stay with it and feel the absence till I get nostalgic about the good times and realise I have to get on with whatever is pending in the meantime.

Notice it's there, and focus on what's more important despite that.

I remind myself that life is meaningless

Remind myself it no longer matters

Let it be. Eventually it'll go away.

Mind over matter stuff ....;)

Wait

It's an emotion, they might not matter anymore but they once did, it's ok to still feel that loss at times.