I noticed that slightly touching the mount of the first mirror on the HeNe probe path makes the beam deflect a lot. So I changed it with a more rigid mirror mount.
I also wanted to clean the mirror (Thorlabs 1/2" Protected silver mirror PF05-03-P01), but I broke it, so I replaced it with a Newport 5103 General Purpose Silver Coated Mirror that I found in Tama.

Then I aligned the HeNe probe using the pinhole. The beam passes through the following positions of the pinhole:

I noticed that the reflection of the first lens on the IU was going up to the chopper. This is very likely to generate noise in phase, so I tilted the lens of the IU.
I also noticed another reflection from the sample that is going to the chopper. I can't tilt the sample, so I solved it putting a simple aperture near the chopper. See picture.

I used the surface reference to align the pump and maximize the AC signal.

I used the new power meter for the pump:
pump power: 74mW , chopper on: 37mW, with surf ref sample: 27mW

I moved the imaging unit to find the maximum of the signal on the surf ref.

The maximum is not in the range of the IU stage. Probably because tilting the lens to move the probe reflection from the chopper, I missed  the focus of the IU telescope.

Therefore I started again the IU alignment. I put the IU stage at 60mm. I found the sharp image of the blade. I looked for the maximum of absorption signal again:

So I put the IU at 70mm.

I made a scan of the surf reference.

I noticed that the DC is not linear with the power of the probe. I measured 6.4V for 1.71mW, and 6.5V for 2.58mW. Then I replaced the LDS9 power supply with the 12V battery and the 2.58mW gave 9V of DC. So I decided to keep the DC below 6V with a OD wheel, and continue using  the LDS9 power supply.

After putting the wheel, I missed the alignment pump/probe, so I used again the  pinhole to center the probe.

Then I made a scan of the surf reference again.

And a scan of the bulk reference. The transmitted power is 20mW (of 37mW incident)