The price for the drive alone seems high. You can get a replacement drive yourself for it for about $40 through OWC. Here is the link:https://eshop.macsales.com/item/Hitachi-LG/HLDSGA31N/
So, you could ask if you can buy the drive yourself and then if he will still replace it for $150.
If for some reason you wanted to replace the drive yourself, then it would essentially be a little more than $40 as you would need to buy the tools needs as well. I will note that it is not an upgrade that is for the faint of heart to do. It is way more complex than just opening up a tower case that you might find on a typical Windows tower, pulling two cables and unscrewing the bracket screws...much more involved than that. To see if you want to attempt it, there are links to the installation videos for the various iMac models under the "Compatibility" tab in the link above. The process will vary depending on which 2009 model you have...you did not specify which (there is the 20" Early 2009, the 24" Early 2009, the 21.5" Late 2009, and the 27" Late 2009). If you want a step by step guide, then I can point you to the appropriate guide on iFixit.com if you tell me which model you have.
The other over all option is to get an external optical drive. This obviously does not require taking the iMac apart. Here are three USB 2.0 options that range from about $40 up to about $50:https://eshop.macsales.com/item/OWC/MRSSDSDT8X/https://eshop.macsales.com/item/OWC/VLU2SD24XS/
If you want a BluRay drive, then there are these two options.https://eshop.macsales.com/item/OWC/MRSSBDL6X/https://eshop.macsales.com/item/OWC/MRSSBDR6X/
Note that first external USB 2.0 CD/DVD drive and both external USB 2.0 BluRay/CD/DVD drives can either operate as USB bus powered drives or with a separately purchased external power adapter. The second external USB 2.0 CD/DVD drive ships with an external power adapter. This is important because for the drives to operate in bus power mode will generally require you to use two USB ports to get enough power. Those drives will ship with a special "Y" USB cables that have two connectors for the iMac side. If you only want to use one USB port, then you likely will need to buy the external power adapter, which are shown on each page for each drive towards the right side as the first item under the "Recommended Items".