Donna Vekic was outplayed by teenager Elisabetta Cocciaretto at the Palermo Ladies Open.
After a record pot of $57.2million in 2019, the USTA has reduced the money on offer to players in this year's edition.
There will be no grudges held by Rafael Nadal against those players who take part in the US Open for prize money.
Top seed Petra Martic cruised through her opening game in Palermo, but Marketa Vondrousova and Elise Mertens were knocked out.
World number two Rafael Nadal will not travel to New York for the US Open after "many thoughts" about the decision.
There were no handshakes, players handling their own towels and less ball kids in Palermo on Monday, but it did not bother Donna Vekic.
With Ashleigh Barty skipping the US Open, Andy Murray expects other stars to do likewise.