Do I respond to birthday card

[quietlifeneeded]

Have had to cut 2 siblings from my life recently and I'll not lie, my life has become so much calmer for doing it.

I've had no contact, blocked on social media etc. Made it very clear to both why I was doing what I was doing.

Both siblings have zero contact with my children or my husband... yet for the first time ever they have both sent him a birthday card.. the usual guffins 'to the best brother in law'..

Am I being paranoid in thinking they have done it to get a response from me?

You're not being paranoid, it's possible that's the motive, but it actually doesn't matter to you why they did it. Unless you're going to have a change of heart about your relationship with them based on a birthday card, pop them in the recycling and continue as you were in peace.