No it doesn't suck money out, but it reduces the rate at which new money is created through borrowing.
Every time a loan is agreed, the value of the ${NATIONAL_CURRENCY} is diluted by a tiny amount. And that tiny dilution is amplified through the economy and has a proportionally larger effect on the price of end-user items which inflate to compensate.
Increasing interest rates is not a lever that directly affects things measured by the CPI, but the idea is that the effects will ripple through the economy and reduce the delta-v of their prices at the end of a very complicated series of gears and pulleys.
It's a bit like trying to refloat a grounded ship by subtly nudging the Moon's orbit to modify the tides.
