I bet the people who inject a staple through a check and into the invoice remittance slip are not people who actually handle the accounts receivables for a company. The people who place a staple through a check are probably only on the accounts payables side.
You can easily deposit a check that has other papers stapled to them. You need to claw off the staple carefully from the check to ensure it doesn’t rip. If you happen to pull too hard, not only can you rip the check, you can also cause bodily harm to yourself and cause blood to spill over the check.
But really, why do people staple the checks to the slips? Why!!!!