Remove remaining ovary tissue?

My cat is in heat a blood test has confirmed this but she is not eating so I feel that I have to have the remains ovary tissue removed

Hi and welcome to TCS!  

I have a couple of questions.  Are you saying your cat was incompletely spayed?   Yes, you should have the remaining tissue removed, but ask your vet when to do so.  Vets try to avoid spaying a cat when she is in heat, although I don't know if that matters in a case like this.

My second question has to do with her not eating.  How long has this been going on?  Cats shouldn't go for more than two days without food as they can come down with hepatic lipidosis, or fatty liver disease.  This is a very serious, even potentially fatal condition.  It's important to get your cat eating again so here are some things to try.

1.  Try putting her food under her right after she wakes up.  Sometimes they eat by instinct.

2.  Try warming her food up.  It will release an aroma that might tempt her to eat.

3.  Try feeding her warm tuna fish, ham, or turkey or chicken baby food (no garlic or onions).  

4.  Try putting toppers on her food like Fortiflora, bonito flakes or crumbled cheese.

5.  Cook her some chicken (no spices) 

6.  Talk to your vet about getting an appetite stimulant.

Here is some more information:
[article="33011"]How To Get Your Cat To Start Eating Again  [/article][article="32998"]Why Has My Cat Stopped Eating And Is It Dangerous  [/article]

This is not all that uncommon, the ovarian tissue is a bit frayed around the edges and can break off and easily be left behind when a cat is spayed, these tissue remnants trigger hormones to kick in and cause heat symptoms, although they think they can, they can not get pregnant.

It is your choice to have them removed, I certainly would as a cat in heat can be a real pain.

I've had 2 cats "re-spayed" and it went fine, no more issues!