The licking and eliminating outside the box reminds me of my previous cat.
She began to lick on our patio stones and poop in the bathtub. A trip to the
vet diagnosed her as hyperthyroid. Maybe have her tested for this?
Hyperthyroidism is common in senior cats.

Judy

She may have a medical problem beyond the UTI. Tell the vet that she is
still peeing outside the box and ask about urine testing and blood work (if
that hasn't already been done). A complete checkup is a good idea with an
older cat anyway.

She probably was having pain (from the UTI) when urinating in the box and
might be associated the pain with the box.  You need to keep the laundry
where she can't get to it until she is retrained back to the box. I'd clean
the floor and the laundry basket well with an enzyme cleaner to make sure
there is no residual odor from her past indiscretions.

You might want to set up an additional box in a different location so she
wouldn't associate that box with the pain she had before. You may also want
to try cat attract kitty litter. If you've had the old litter box for a
while you might want to consider replacing it. Plastic can acquire an odor
after a while that won't be eliminated by a simple cleaning.

An older cat might be having trouble getting in and out of a box if the
sides are too high.

Make sure you praise her when you see her using the box.

W