とぎしる is the reading favored by shinmeikai, oukoku, and meikyo, so it should probably lead.

Google N-gram Corpus Counts
╭─ーーーー─┬────────┬───────╮
│ とぎ汁　 │ 61,044 │ 88.2% │
│ 研ぎ汁　 │  7,282 │ 10.5% │ 🡠 adding (meikyo)
│ 磨ぎ汁　 │    589 │  0.9% │ 🡠 rK (daijr/s, koj, gg5, and others)
│ 磨汁　　 │     74 │  0.1% │ 🡠 dropping (only shinmeikai and nikk, which always have these rare okurigana-less forms)
│ 研汁　　 │     59 │  0.1% │
│ とぎじる │     83 │  0.1% │
│ とぎしる │     42 │  0.1% │
╰─ーーーー─┴────────┴───────╯

@@ -8 +8 @@
-<keb>磨ぎ汁</keb>
+<keb>研ぎ汁</keb>
@@ -11 +11,2 @@
-<keb>磨汁</keb>
+<keb>磨ぎ汁</keb>
+<ke_inf>&rK;</ke_inf>
@@ -14 +15 @@
-<reb>とぎじる</reb>
+<reb>とぎしる</reb>
@@ -17 +18 @@
-<reb>とぎしる</reb>
+<reb>とぎじる</reb>