Loose caliper on Integra?

95 Teg LS....

Did a complete brake job, including two new rear calipers (old ones were
binding up pretty good). About a month after I finished the job, I'm hearing
a pretty loud knocking from the rear when going slow over bumps. Noise goes
away when I depress brake pedal or pull on e-brake handle a few clicks. So I
dive underneath and start pulling on things to see what's loose. Get to the
calipers and when I pulled on them by the brake hose boss and giggle, they
deflect a good 1/8 -1/4 of an inch back and forth!

That's not right, is it? No car I've ever worked on had their calipers move
at all, even when retracted. I'm thinking the rebuilder did a lousy job and
used wrong hardware...surprising ,but I guess possible.

Thoughts?