Dumping firmware/software...and/or reflashing??

In that top picture it does look like a "44".

If...

• It is an SPI programmable processor (like an ATtiny44)
• You can get some connections to it
• RESET has not been disabled
• SPI programming has not been disabled

...you can determine exactly which processor it is by reading the signature bytes. With the exception of the physical connections, making the attempt is very unlikely to damage anything. Just include series resistors; 220 ohms works well.