It's influential. That's why.
Mothers-in-law are amicable with the son-in-law, even though he doesn't thank them for their help.
Also, the event of "thanking" hasn't even happened. If you had said "a pesar de que él no les agredece" instead, it would mean the son-in-law NEVER thanks the mothers-in-law.
So, a quite better translation could be
Mothers-in-law are nice to their son-in-law even though he doesn't thank her for her help
A pesar de que mi madre me pegue con piedras, la quiero.
I love my mother even if she hits me with rocks.
or even better translated as
Even if my mother hit me with rocks, I love her.
The subjunctive mood allows this to be a bit passive, indicating that he's not always hit with rocks. That, in the event he is hit with rocks by his mother, he would still love her. It's really difficult to translate into English since there is no subjunctive mood in English. It's even more difficult to explain.
All in all, I think the use of the subjunctive in your sentence falls into the mood of influence.
Typically, when using any of the following, you'll find yourself using the subjunctive mood.
Ordenar, mandar, querer, desear, decir (ordenar), insistir, sugerir, permitir, dejar, esperar, prohibir,
oponerse a, impedir, preferir, aconsejar, rogar, recomendar, suplicar, temer, gustar, agradar, alegrarse,
sorprender, molestar, entusiasmar, enojarse, etc.