The mode looks quite terrible in the plot, but in reality it is an illusion of the plot.
The actual TEM00 content in this beam is ~99.7%
Based on the above document, you can calculate power coupling between two elliptic gaussian modes.
Give the parameters of one beam as
zRy1 = pi*(2.77e-3)^2 / 1064e-9
z1y = 3.37
zRx1 = pi*(2.47e-3)^2 / 1064e-9
z1x = 4.15
Then, assume a round beam for the other.
zRx2 = zRy2 = zR
z2x = z2y = z0
Then run the optimizer to find the maximum for the quantity |C|^2
|C|^2 max: 0.9967
zR = 20.19
z0 = 3.804