interpolation of scattered data, griddata and gridfit returns bad values

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Hello all
I am having a problem with interpolation and contour plot which is killing me. I would appreciate very much if you could help me with that.
Basically, I have experimental results for the pressure values over a surface. This means that I have vectors x and y which are locations on the surface and on each location, I have a value for pressure. The surface is square. The data are very scattered and the concentration of points on one corner is much higher.
I want to interpolate my data on all the locations on the surface and plot the contour.
I have attached a picture of the actual points and the exact pressure values read during the experiments.
For interpolating the data, I have used both griddata and gridfit.
1- For using the griddata I have to use 'V4' method because on some points on the surface I do not have any values and other methods returns 'NANs'. However, when I use griddata, I get some silly values on some points. I have attached a contour plot using griddata showing the bad values.
2- I have tried grisfit hoping that it will give me better results but the I get very similar pattern to what I get from griddata. I have played with all the parameteres that can be changed in gridfit and I was not able to get a good result.
3- I have to just mention that I have played with my mesh size a lot too and again no improvement!!
I would appreciate it very much if someone can help me with that. I just do not know what can cause this problem and how I can handle that.
Much Appreciated Maryam

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