(I suspect this question refers to your TRS retirement, where some TRS education systems are allowed set up their pension system outside of the US Govt system and do not withhold SS or Medicare taxes.)
IF..if the "surcharges" you are asking about are SS and Medicare taxes that show on your new job W-2....then NO. Those employment taxes cannot be deducted or refunded. (some exceptions for a person with multiple W-2 jobs earning over ~$132,900 (2019) where SS&Medicare was deducted on those W-2 forms. $137,700 for 2020)
But, IF you continue to work for employers that withhold SS and Medicare taxes, and if you earn enough credits over 10 years of working for those employers, then you will also be eligible to receive SS (and possibly Medicare benefits too) . Max number of Credits is 4 per year and is based on how much you earned that year.
(It used to be based on working every quarter of the year...not sure they do that anymore).
https://www.ssa.gov/OACT/COLA/QC.html
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If you worked for outside W-2 employers, before or during your time as a teacher, then you may already have some credits banked with SS and you may not have as many credits to earn to qualify for full SS.
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Now, if you worked for an education system in TX that did withhold SS and Medicare taxes.....your continued work outside may just increase your eventual SS benefits...a lot depends on your earning levels each year.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
