Thanks for all the feedback.
I hadn't thought to look and see if Harry Olitsky actually used his passport to travel to Europe, and then back to the US, so I didn't know that he traveled on the SS Kaiser Wilhelm in 1908. He must have already booked his passage prior to applying for the passport. I had previously checked out this ship before, and found on SteveMorse that it never sailed out of Hamburg, but only out of Bremen.
Someone privately wrote me that they found a B. Olitz living in Philadelphia in the early 1900s, so that may possibly be the brother of Harry Olitsky, so I'll follow up on that.
As for the surname Ulitsky vs. Olitsky - I have seen the spelling Ulitsky used, and I believe on Jewishgen it comes up when you enter the 'Sounds Like' search option for Olitsky. In US records, I have seen the same family with the spellings Olitsky, Ulitsky, Eletsky, Olatsky, and others. Of course, these early immigrants were having their names written down by others, and they would not have known how often different spellings were being used. Interestingly, my great grandfather only used Olitsky or Olitzky.
The surname means from Olita (now Alytus, Lithuania).
Lock/Lak/Lok and Kalon in Zagare/Joniskis/Gruzdziai, Lithuania
Trisinsky/Trushinsky/Sturisky and Leybman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lewin/Levin in Trenton, New Jersey and Lida/Vilna gub., Belarus