My mother was talking on the phone and I heard her say “I swear to my kids” I asked her about it and she said she knows it’s haram but she just wanted the person on the phone to believe her. I told her it was shirk and she said “Astaghfurillah, God forgive me.” Does it count as shirk towards her even if she didn't know? And should she do Tawbah?
She will have to sincerely repent, and say the Shahadah before repenting. You can research the conditions of sincere repentance.
Or she can recite the dua:
"Allahumma ini a'oudho bika un ushrika bika wa ana a'lamu wa astaghfiruka lima la a' lamu" (O Allah I seek refuge In you from knowingly associating partners with you and I seek forgiveness from that which I do not know.) Al Adab Al Mufra 716 ( Sahih - Al Albani)
And Allah knows best.