Is there any connection between the presence of henna tattoos on the skin and jinn entering the body?

Firstly: 

Dyeing the hands and feet with henna is something mustahabb (encouraged) for women, unlike men. A number of hadeeths indicate that it is mustahabb, such as that narrated by Abu Dawood (4166) from ‘Aa’ishah (may Allah be pleased with her) who said: A woman gestured from behind a screen, with a letter to the Messenger of Allah (blessings and peace of Allah be upon him) in her hand. The Messenger of Allah (blessings and peace of Allah be upon him) withdrew his hand and said: “I do not know whether it is the hand of a man or a woman.” She said: It is a woman. He said: “If you were a woman, you would have changed your nails,” meaning, with henna.

Classed as hasan by al-Albaani in Saheeh Abi Dawood 

It says in ‘Awn al-Ma‘bood: 

The hadeeth indicates that it is highly encouraged for women to dye their hands with henna. End quote. 

Abu Dawood (4928) narrated from Abu Hurayrah (may Allah be pleased with him) that an effeminate man who had dyed his hands and feet with henna was brought to the Prophet (blessings and peace of Allah be upon him). The Prophet (blessings and peace of Allah be upon him ) said: “What is the matter with him?” They said: O Messenger of Allah, he imitates women. He ordered that he be banished to al-Naqee‘.

Classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked: 

Is it obligatory for a woman to put henna on her hands, because some people say that a woman is imitating men if she does not put henna on her hands? 

He replied: 

Undoubtedly dyeing her hands with henna is mustahabb. There are some hadeeths concerning that which are somewhat da‘eef (weak), but it is better for her to dye them with henna. As to whether that is obligatory or it is haraam for her to leave her hands white, I do not know of any basis for saying that. But it is better and preferable for her to dye them with henna, so that they will not resemble the hands of a man. This is what is better and is preferable, because there are hadeeths which speak of this, and because it is part of the Sunnah that is well-known among women and it was customary at the time of the Prophet (blessings and peace of Allah be upon him) and afterwards to dye the hands with henna, and it is preferable for women. End quote. 

http://www.binbaz.org.sa/mat/8866

See also the answers to questions no. 105417 and 99629 

Secondly: 

The view that dyeing the hands with henna or these designs that are drawn with it on the hands and feet of women, are a cause of attracting the jinn and of them entering the human body – all of that is something for which there is no evidence, so no attention should be paid to it. If any of that were true, Islam would not have granted a concession allowing the use of henna. 

Please see the answer to question no. 10513 for information on how to protect ourselves from the harm of the jinn. 

And Allah knows best.