Let's break down our passage.

1. printers/scanners make faking checks easier
2. to deter fakes, banks will issue small-dot checks
3. scanning/printing small-dot checks doesn't work

We're asked to identify an assumption of the plan, and as the logic given in the passage is extremely clear, we'll first try to infer it and only then look to the answers.
This is a Precise approach.

In particular, there are 2 main claims. The first is that the small-dot checks will deter fakes. This assumes that, currently, fakes are created by scanning and subsequently printing existing checks, which is nowhere mentioned in the passage and is therefore a likely answer. The other main claim is that today's printers are technically unable to scan and print the 'small-dot' checks. For this to be relevant, we need to assume that tomorrow's printers won't be significantly better than today's.

Looking over our answers, (E) is equivalent to the second assumption we identified and is our best answer.