How does this 433Mhz garage remote control work without an antenna?
In fact, it has an antenna.

Best guess would be the track running along the top (in your picture, left) edge of the PCB.

What you've pictured is a transmitter, probably based on a Surface Acoustic Wave (SAW) resonator - the metal can you see in the picture.

Since you haven't pictured the internals of your particular system's receiver, it is not possible to say what type it is.

In the pair you picture below the transmitter is again a SAW, and the receiver has the visual appearance of a common cheap design using a regenerative scheme.  Such receivers will toggle their data output in the absence of signal - accomplishing meaningful communication requires a circuit (today typically MCU code) to look for a specific meaningful pattern.

You may find it more worthwhile to build a system around one of the SPI-based sub-GHz radios from SiLabs, Ti, etc which have the frequency set by software and can be configured with a meaningful squelch and to slice the data nicely for presentation as either synchronous samples or in an actual packet buffer.  Granted, they take some software effort to configure, and there are available codebases for dealing with the messy output of a cheap regen.