It is indeed a tea strainer, but not quite for use as described above. The tea is brewed from loose leaf in a teapot but when your pour it you don’t want those leaves in your cup. You tilt the strainer so the mesh bowl sits over your cup, pour the tea through it, and the mesh retains any stray leaves. When you set the thing back on the table, the mesh bowl tilts back to its normal position and the pan at the bottom catches any drips.
It’s by Johann Beck of Schwäbisch Gmünd in Germany. The dates for this maker are uncertain, but your piece has the national ‘Crescent and crown’ (Halbmond und Reichskrone) which was in use from 1886 and became a compulsory mark from 1888.
[PS: For black tea, the water should be as near boiling point as possible if you want it to brew properly. 'Pinky extension' is optional].
