Single transistor IR repeater
C5 was not installed on the board, what you're seeing is just the drop of glue that was supposed to hold it during soldering. They probably decided the circuit would work without it, so they configured the pick and place machine not to place it, but they didn't bother to modify the configuration of the machine that dispenses the drops of glue.

Now, looking at the schematic, this shouldn't work. The IR signal is modulated: it is not simply a LED blinking on/off for each bit, rather the IR LED blinks at 38kHz for the duration of a "1" bit, and it stays off for a "0" bit. The TSOP receiver demodulates the IR signal and ouptuts bits, not the 38kHz carrier.

If the repeater works, then something on the board is turning the bits back into modulated 38kHz signal. Either the transistor is not a transistor but an IC, or the "LED" that it uses to transmit is not actually a LED but an IR transmitter which will generate 38kHz IR pulses when it is on. Or the TSOP4838 isn't a TSOP4838 but something else that outputs not demodulated signal.

Either way, there's a component in there that isn't what you think it is, that's why your attempt to replicate it fails.