In my experience, all counters are noisy, but some counters are noisier than others
Price and brand doesn't seem to be a significant factor. I guess when you've got that many TTL signals bouncing about in there, it's not surprising. Whether the plastic construction makes it worse is an interesting question, but based on my experiences, it might not be a worthwhile exercise given how much leaks out of counters using metal enclosures. Having said that, an awful lot of the counting logic is contained within a single IC, so perhaps it's not as good at creating RF noise as some of the more discrete units out there...
I don't suppose you know of anyone locally who could lend you a different unit? That might give some indication of how yours compares, and whether it's worth trying to improve it...