The surname spelled "Zielis" is not found in the current online phone book for Lithuania. There is one listing for a "Zielis^" (a very unusual ending for a Lithuanian name that is pronounced something like ZiAI-lish or ZEH-lish).
However, there are 321 listings for the surname spelled "Z^ilius" (pronounced ZHI-loos) including the women's endings "-ute" and "-iene" used for unmarried women and married women respectively. So the odds seem tilted very much towards the much more common "Z^ilius" since there are no listings for "Zilius."
The Lithuanian alphabet includes two letters "z" (as well as two letters "c" and "s"): one has a little birdie over it (typed "z^" on non-Baltic keyboards) and is pronounced "zh" as in the English word "azure"; the other does not have any mark over it and is pronounced "z" as in the English word "zoo."
The "s" with a birdie over it is pronounced in Lithuanian "sh" as in the English word "shout." But without that birdie, it is pronounced as in the English word "state."
The surnames for women have a different ending than their husbands or fathers. For names ending in "-is", the ending for unmarried girls or women is "-yte". All unmarried women's names end in "-iene" regardless of the ending on their husbands' names.
The "correct" spelling of anyone's name is what he or she says it is, not what nuns or teachers say. Immigrants to America (and other countries) usually modified the Lithuanian spelling and pronunciation of their names to suit the new environment they lived in, where English was the dominant language. So Lithuanians might change the "z^" to plain "z" because, when English speakers saw a "z" whether it had a mark over it or not, they usually pronounced it as it most commonly appears, as in "zoo". So Frank's parents might well accept that pronunciation to save explaining what I've just explained. Some immigrants with this surname might spell their name "Zhilius" to indicate that "z^" sound and keep the phonetics close to Lithuanian. I could easily see a Lithuanian immigrant with this surname simplifying it to "Zilus" or "Zilis". The Lithuanian "-ius" is pronounced with just the barest hint of the "i" sound before the "u", so to the American ear it would sound simply like "oos".
There is no way to determine how many people carry the surname Zilius in America. But I did a search of ancestry.com of all people with this surname in the 1930 U.S. Census and came up with the following list:
Ranked Search Results - 1930 United States Federal Census
You searched for Zilius
Name; Home in 1930 (town, state); Birth Year; Birthplace (if given)
Edward Zilius; Penn, PA; abt 1874; Germany
Ignas Zilius; Peru, ME; abt 1876; Lithuania
John Zilius; Huntingdon, PA; abt 1876; Pennsylvania
Anna Zilius; Chicago, IL; abt 1882; Lithuania
Joseph Zilius; Lima, OH; abt 1882; Lithuania
Grace E Zilius; Huntingdon, PA; abt 1885
George Zilius; Kenosha, WI; abt 1893l; Lithuania
Jonas Zilius; Boston, MA; abt 1894; Lithuania
Joseph Zilius; Paterson, NJ; abt 1894; Lithuania
Veronica Zilius; Paterson, NJ; abt 1896
Charles E Zilius; Huntingdon, PA; abt 1908
Blanche B Zilius; Huntingdon, PA; abt 1911
Bruno Zilius; Chicago, IL; abt 1911
Florence Zilius; Paterson, NJ; abt 1928
My guess is that there is a fair chance that some of these folks were related to your grandfather, however distantly.