One idiom means to have sex (CLEARLY not the meaning here).
If you wanted to do a lot of calculations to try to figure out where to save money, before the days of computer, you'd need a sharp pencil and an eraser. So perhaps the writer was saying that they need to buckle down and figure out where the savings can come from. It's not really an idiom that way.
It's also possible it was being used as a figure of speech at all - they'll save money in little ways, doing things like using pencils down to the nub rather than using a new one.
I've never heard it used to mean "get a better deal."