Yes, it matters.
First, reducing what they take is more efficient than inventing new bureaucracy to send out checks.
Second, I cannot rely on a random bonus but I can rely on the taxation tables therefore I am more likely to plan on doing something useful with reduction.
It's the exact contrary of bureaucracy. Bureaucracy is deciding for the poor what they are allowed to do with the money on the wrong assumption that they wouldn't know better than you what to do with it. In fact the less money you have, the more careful you are with it. Obviously. And at the extreme end of the spectrum, if you are rich like Elon Musk, you spend 44 billions on something dumb.
No, this depends on the specifics. If they are sending every tax filer an extra 1000 then that would be very efficient (setting aside those people who do not file federal taxes). If the tax reduction is complex, requires knowledge of complicated eligibility criteria, going in person to a local SS office or for a notary public, it's very inefficient.
As a general rule, then, this claim is bogus.
If we send every person a check it requires, at the very least, envelopes and postage.
My first claim is not about the efficiency of how the money is used by the beneficiaries. My claim is about the efficiency of getting the money gets into people's hands in the first place.
We already have an efficient system for sending out checks—the Social Security Administration