Salam Sis.
To answer, lets refer to some hadiths:
Narrated ‘Abdullah bin Yazid Al-Ansari: “The Prophet forbade robbery (taking away what belongs to others without their permission), and also forbade mutilation (or maiming) of bodies.” (Translation of Sahih Bukhari, Oppressions, Volume 3, Book 43, Number 654)
Narrated ‘Abdullah: ”Allah has cursed those women who practise tattooing and those who, get themselves tattooed and those who pluck their eyebrows , and those who create a space between their teeth artificially to look beautiful, and such women as change the features created by Allah. ”(Translation of Sahih Bukhari, Dress, Volume 7, Book 72, Number 815) (Rasul s.a.w specified women in this hadith because tattooing was more famous amongst women, previously.)
According to these Hadiths, having tattoos are prohibited by the religion because you are altering god’s creation. Same goes for other unnecessary interference, alteration and mutilation of Allah’s creation.
Tattoo vs. Wudhu:
Tattoo does not invalidate wudhu nor prayers as the colour pigments are said to be injected beneath the skin (which explains the complexity of removing). By informing this, we are in no way advocating tattoos. We are just saying that having tattoos is not a valid reason for one to skip prayers! haha. :D
There is a different view from some scholars with regards to this matter (permissibility of tattoo in Islam). However when I was researching, the arguments weren’t backed up by daleels. Hence, I dare not say it is permissible. To be sure, do cross refer with multiple religious articles and trusted teachers.
Wallahua’lam. :)