How do I implement the CDF wavelet inverse?
To the contrary, the odd tap filters allow you to keep everything perfectly symmetric. If you make the filter centered at $0$, then the application of the filter at position $i$ requires a symmetric range of coefficients around $i$.

All 2-channel wavelets will produce a quad-tree decomposition of a 2D image, regardless of tap length. The only complication of longer, non-trivial wavelet filter banks is the treatment of the boundaries. Here one has an advantage in using symmetric filters. (Symmetric and orthogonal wavelet filters exist for 3-channel, 4-channel wavelets and so on. See articles by Heller, Belogay/Wang, Turcajeva.)

If you continue the image by mirroring at the boundaries, the transformed image will also have odd or even symmetry at the boundaries so that the size of the transformed image can be kept equal to the size of the original image.

In the reconstruction process, you have to reconstruct those mirrored coefficients in the bands and then apply the centered filters to obtain the original image back.