The courier may not accept your pearls to be shipped out because any fishery products has to have the permit of the Bureau of Fisheries and Aquatic Resources and you do not have a finished jewelry but undrilled pearls which may be considered a fishery product.
Under the Philippine Fisheries Code Article 4 Section 61d, "No person, shall import and/or export fishery products of whatever size, stage or form for any purpose without securing a permit from the department."
Here is the link and a screen cap of the provision from the Bureau of fisheries website.
http://www.bfar.da.gov.ph/lawAndRegulation.jsp?id=2#post
It may be as simple as getting a permit from the Bureau. You may opt to write them an email and make an inquiry at
info@bfar.da.gov.ph.
On your pearls, I haven't encountered in Manila someone selling South Seas from a street vendor. Usually they are in shops or stalls. Your pearls look like South Seas to me but they seem not to have the dark golden colors and many are not rounds. I see some of them are bi-colored. They are still nice as jewelry but there is a high premium on round and unblemished pearls with good size. Because of the shape, I assume they are cultured, and if the total number of pearls you invested in are the number in the photos, flying to Manila from the US may cost you more than the actual value of the pearls.
On going out of the Philippines, there are many tourists that take South Sea Pearls out of the country. Take people that buy from Greenhills alone. Many make purchases of undrilled pearls or in jewelry, but ofcourse the pearls can be from China, Australia, Indonesia, Japan, French Polynesia, etc.