The problem is not that the circuit is only 15 Amp, as that is fine for many dishwashers. There are two problems:
Hardwired loads > 50% capacity
Technically, this may not be a problem. If the dishwasher is plug-in then it is not a permanent load (arguably, though practically speaking it is). If there are hardwired loads > 50% of the circuit capacity (and that will almost definitely be the case for a dishwasher because of the heater used for water heating and drying), then you can't have additional receptacles on the same circuit.
Dedicated Countertop Receptacles
This is the big problem. Current code requires 2 dedicated 20 Amp circuits for countertop receptacles in the kitchen. There are few exceptions, but not for major appliances like a dishwasher. If you currently have 15 Amp circuits, you don't have to upgrade them. If you currently have shared circuits, you don't have to change them. But you can't make things worse.
Adding receptacles below or, alternatively, a hardwired dishwasher, means that the circuit is now shared in a way it was not shared before.
Removing the receptacles so that the circuit is only used for the dishwasher might work, except that in most cases by doing so you will now violate the rules for how many countertop receptacles you need to have and where they need to be located (the specifics depend on size/location of counters).