UK visa application for a person who had overstayed earlier

About 3 years back my parents, both Indian citizens visited my sister, a UK citizen. About a week before they were supposed to return, my father was hospitalised. The Visa was was about to expire in 2 weeks and my sister applied for a renewal of visa, citing the reason that

1) my father is not in a position to travel ( backed up by supporting letters of his treating doctors) and

2) my mother needs to be with my father for any assistance.

Subsequently, after close to a months hospitalisation, my father passed away. Visa had expired by then. His funeral also was done in UK.

My mother could not return as her visa renewal application was still under process. His passing away was informed to the visa office and after about 2-3 months, my mother was asked to re apply once more as the original reason did not hold good anymore (since my father was no more). She re apllied and after considerable time (about 15 months from the original application), she was called for a hearing and her application was rejected.

She payed for her ticket and traveled back. I am told that she also got a letter (not sure from whom) which said that as my father's final resting place is in UK, she can visit again. Unfortunately this letter is lost now.

She is planning to travel soon so that she can be there for his anniversary.

Will she face any hurdles in getting the visa approved due to the overstay? Anything that needs to be done special during the application to indicate her overstay and return?

It will be a visiting visa (6 months)