In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Answering your question, the Fatwa Center at Islam Q and A, states:
You do not have to use something to lift the toenail so that the water can pass beneath it; rather that is a kind of strictness that is not acceptable according to Islamic teachings.
If the person who is doing wudu washes the parts of his body in an ordinary manner, then he has obeyed the command of Allah and has done what is required of him.
If it so happens that there is a small amount of anything under the nail that the water does not reach, then it comes under the heading of negligible matters that are pardoned, such as dirt under the nails and cracks in the feet. The one who is doing wudu does not have to make sure that water enters every single crack or to check them and examine them.
It says in Matalib uli an-Nuha (1/116):
“A small amount of dirt under the nails and the like does not matter, and the same applies to the inside of the nose, even if it prevents water reaching where it should, because these are things that usually happen a great deal, and if wudu were not valid in the case of such matters, then the Prophet (peace be upon him) would have explained it, because it was not permissible for him to delay explaining at the time when such knowledge was needed.
To that – i.e., the issue of a small amount of dirt – Sheikh Taqi Ad-Deen Ibn Taymiyyah (may Allah have mercy on him) added every small thing that could prevent water reaching the skin, such as dried blood or dough on any part of the body. This was the view he favored by analogy with dirt under the nails. That also includes cracks that may appear on some parts of the body.”
Almighty Allah knows best.