any help that you could give her is highly appreciated vs any help that you could give her is greatly appreciated.

Some examples from the web:

• Look, any help that-that you could give would be greatly appreciated.
• Mrs. Keeler, any help you could give us would be greatly appreciated.
• I'd be honored to take any help you could give me.
• If there is any help that I could give, I would be only too happy.
• The best help you could give me is to cover my back.
• See, I need a little help if you could give some.
• But in the end, she needed more help than I could give her.
• So any help that you can give me, please.
• There's nothing that you could give me that I would want.
• I thought maybe that you could give me some answers.
• We'd appreciate any information that you could give us.
• So any help that you can give me, please.
• And we were hoping that you could give us a lift out there.
• I bet that you could give me a dozen examples of societies that have kild their own young.
• I just needed you to shut up so that you could give me a ride to the hospital, and I won't bleed to death in the street.
• But when I act on that assumption to try and protect you from unhappiness, it does seem that you could give me some credit for...
• It is perhaps the best punishment for this violent dictatorship and the best gift that you could give the elected president of Burma, Mrs Aung San Suu Kyi.
• Maybe you could give her a horrible rash or something for the wedding.
• Her Ladyship wondered if you could give her an account of the day.
• Tomorrow's vote will determine whether we have any help to give.

Some examples from the web:

• Look, any help that-that you could give would be greatly appreciated.
• Mrs. Keeler, any help you could give us would be greatly appreciated.
• I'd be honored to take any help you could give me.
• If there is any help that I could give, I would be only too happy.
• The best help you could give me is to cover my back.
• See, I need a little help if you could give some.
• But in the end, she needed more help than I could give her.
• So any help that you can give me, please.
• There's nothing that you could give me that I would want.
• I thought maybe that you could give me some answers.
• We'd appreciate any information that you could give us.
• So any help that you can give me, please.
• And we were hoping that you could give us a lift out there.
• I bet that you could give me a dozen examples of societies that have kild their own young.
• I just needed you to shut up so that you could give me a ride to the hospital, and I won't bleed to death in the street.
• But when I act on that assumption to try and protect you from unhappiness, it does seem that you could give me some credit for...
• It is perhaps the best punishment for this violent dictatorship and the best gift that you could give the elected president of Burma, Mrs Aung San Suu Kyi.
• Maybe you could give her a horrible rash or something for the wedding.
• Her Ladyship wondered if you could give her an account of the day.
• Tomorrow's vote will determine whether we have any help to give.