Karma binds everyone including God, when He is in human form. Curses are invited through karmas that affect others negatively. Even good actions can sometimes hurt people and can invite curse – so we have to be very conscious while performing actions, that we do so without hurting or harming others.
Sin is different from curse. While sins can be removed or mitigated through Prayaschitha karmas, curses can be removed only by the person who utters it or by the Tapas of great souls or Gurus; or by a series of actions involving confession, repentance, expiation and asking for forgiveness from the person who uttered the curse.
This can be easily understood from a famous curse from the Mahabharata – the curse cast upon Krishna. After the battle of Kurukshetra, when Krishna went to console a distraught Gandhari, the mother of the 100 Kauravas, she flinched in pain. She cursed Krishna that just as he schemed to kill her sons and end her bloodline, his bloodline too would end. Krishna not only died an untimely death, but his entire clan also killed each other through infighting.
It is very important to recall everyday in our prayer all the bad or harmful actions we have done that day and ask for forgiveness to God.
This is the main purpose of Nithyakarma (or daily worship) be it Sandhyavandhanam, daily poojas, going to Church on every Sunday by Christians or doing regular Pratikraman by Jains or many times daily Namas by Muslims or any other daily or regular or periodic procedures by other religions. All religions get united on this value.
By removing curses and sins on a daily basis, we maintain the balance of karmas to ensure at least a human birth in next life and not a lower form of life.
Learning the Vedantha or the Bhagavad Gita; or attending a satsang is not an excuse for not doing Nithyakarma or Upasana.
As long as we perform actions in the transactional world which involves dealing with people, the possibility of harming or hurting someone will always be there, unconsciously or consciously, caused by deliberate actions or triggered by our Vasanas and Samskaras. Therefore we need to pray regularly, perform Nithyakarmas or Upasana (Japa) to maintain the balance of karmas until we enter the real Sanyasa Ashrama, to meditate on the Brahman without worldly attachments.
Hope it is clear.