Many people think dyed freshwater pearls are Tahitians; they are often sold deceptively as such.
The white pearls would benefit from a bath and probably also restringing. They will look more lustrous then. Pearls and thread accumulate grime from contact with skin, cosmetics/lotions. air pollution. The silk thread becomes comes weak when it's old and dirty, and can break.
To give them a bath, fill a bowl with some distilled water (which I recommend to avoid both chlorine and hard water minerals that can interact with soap to form a sticky scum) and swish some mild soap in the water. Soak the pearls in the soapy water for 15 minutes or so, then wipe them clean with a soft cloth, soft brush or swabs in the hard to reach places. Then rinse them in more distilled water, and lay them on a towel to dry for 24 hours. (The silk inside the drill holes dries slowly.)
To restring, if you would like to try doing it yourself (many of us do), see my tutorial on the Lowly Beaders' Club. And there are also other posts with videos.
How to string (or restring) your pearls on doubled Pattye's Serafil, Beaders Secret, and Power Pro
This is not hard-- really! It is harder to describe it than to do it. Anyone can learn to string their own pearls!
If after reading through this, it sounds too daunting, I suggest making a mini-strand for practice first. Make one 12-15 pearls long just so you can practice how to knot the end 3 pearls on each side and attach the clasps; the middle pearls are easy to knot.
To just practice knotting (without bothering with clasps), make an overhand knot, string on a pearl (or...