Here is the information they provided on the origin of the word:

"Ruthless" can be defined as "without ruth" or "having no ruth." So what, then, is ruth? The noun "ruth," which is now considerably less common than "ruthless," means "compassion for the misery of another," "sorrow for one's own faults," or "remorse." And, just as it is possible for one to be without ruth, it is also possible to be full of ruth. The antonym of "ruthless" is "ruthful," meaning "full of ruth" or "tender." "Ruthful" can also mean "full of sorrow" or "causing sorrow." "Ruth" can be traced back to the Middle English noun "ruthe," itself from "ruen," meaning "to rue" or "to feel regret, remorse, or sorrow."

When we read the Biblical story of "Ruth" we also find "compassion" and "sorrow".

Ruth was a Moabitess, a woman of the people of Moab, (Ruth 1:4) who was married to an Israelite man, Mahlon (Ruth 4:10).  While living in Moab, Mahlon died leaving Ruth a widow.  Thus we find sorrow in the book of Ruth.

Mahlon's mother was named Naomi and she was also a widow.  Rather than return to her own people when her husband died, Ruth clung to Naomi (Ruth 1:14) and returned with her to the Land of Israel (Ruth 1:22).

Through a series of events, Ruth is married to another Israelite named Boaz (Ruth 4:13) who had compassion on her.  Their son was named Obed who was the father of Jesse, the father of King David (Ruth 4:17).

Those who are ruthless are without compassion and without sorrow.  The Messiah Yeshua was a descendant of Ruth and was a man of sorrows and acquainted with grief (Isaiah 53:3) and yet He was full of compassion (Psalm 78:38, Psalm 85:16, Luke 7:13).

Blessed be the Word of G-d that contains Ruth and the Lord G-d of Israel who has ruth and takes pity on us.

The Verse by Verse Ministry has an excellent teaching on the book of Ruth.  I definitely recommend it.