The Gilinskys had 5 girls, Chaya Riva, Shayla, Sora Feigel, Yudis, and Fruma Devasha (B.1884). Gertie died when she was in her 30s and Rafuel died when he was in his 40s. Their daughter Chaya Riva raised the children. She married a man named Harry Grimm. 
Barbara Levy

Based on hits on the JGFF and the LItvak SIG database, I would guess Svencionys.

Steve Stein

I've looked at JGFF and the LitvakSIG databases and I haven't found them. I wrote to a number of researchers in the JGFF, and they haven't come upon them either. I know that Svencionys is a good guess because there were a lot of Gilinskys there, but I also have not found them there.

Barbara Levy

Hi Barbara:

I have gilinski (with i) in my family. Yishie Gilinski married Chaya Sragovicz, who was my great aunt. In my records, I have that he was born in Poluse, Ignalina, Lithuania. 
--

Lia Sragovicz

Stephen,
By the way, most of their children came to the US. It's not clear when, but I know that Fruma was here in 1907, because she was married in Nashua, New Hampshire. Sora Feigel died in childbirth. I know the least about Shayla.
Barbara Levy