We like covered waste receptacles for hand towels that have a plastic bag liner and are hands-free, typically by means of a foot pedal. The cost is negligible as compared to open trash bins; and this method is more sanitary if for no other reason than the fact that the used, potentially dirty, paper towels are less likely to escape and there is no direct personnel contact with the receptacle. It is neater and tidier too!
I did a quick check of SQF code and 21 CFR Part 110.
SQF 11.3.2 Hand Washing says, "Paper towels in a hands free cleanable dispenser; and; A means of containing used paper towels."
The relevant implementation guidance says, "Where alternative methods of hand-drying are preferred (e.g. high-speed air dryers). Their use must be justified and their effectiveness validated (refer 184.108.40.206)."
The relevant auditing guidance says: " There are paper towels available at hand wash stations; There are containers for used paper towels at hand wash stations;"
SQF 11.3.9 Sanitary Facilities refers the reader to the above section when discussing hand washing and paper towels.
SQF 11.4.1 Staff Engaged in Food Handling and Processing Operations says, "Waste shall be contained in the bins identified for this purpose and removed from the processing area on a regular basis and not left to accumulate;"
There is more about waste removal in SQF 11.9.1 Dry and Liquid Waster Removal, but nothing that addresses your concern.
21 CFR Part 110 § 110.37 Sanitary facilities and controls (e) Hand Washing Facilities says:
(e) Hand-washing facilities. Hand-washing facilities shall be adequate and convenient and be furnished with running water at a suitable temperature. Compliance with this requirement may be accomplished by providing:
(3) Sanitary towel service or suitable drying devices.
All that said, being right about the FDA and SQF code may not help you much with a determined auditor or an uncomfortable potential customer.