lick with tongue, taste
舔 centers on using the tongue to touch or sample something: licking or tasting. The two meanings are closely linked, as tasting often involves licking.
舔 combines 舌 (tongue) with 忝, which likely contributes the sound. The character is a phono-semantic compound expressing the action of the tongue.
The left side is a tongue 舌, and the right side 忝 looks like a person leaning over a bowl. Imagine sticking out your tongue to lick or taste something from that bowl.
For テン, picture the number ten (テン) tongues all licking the same bowl at once: ten -> テン, and the scene is a chaotic taste test.