Turmeric is a supplement recommended for the relief of inflammation in many chronic conditions. It is, of course, a spice used in curries.
When taken as a supplement levels are significantly higher than those used for culinary purposes.
This is the information on compatibility with breastfeeding that I found in LactMed
https://www.ncbi.nlm.nih.gov/books/NBK501846/ (the emphasis is my own) :
Summary of Use during Lactation
Turmeric (Curcuma longa) rhizome contains curcuminoids such as curcumin. No data exist on the excretion of any components of turmeric into breastmilk or on the safety and efficacy of turmeric in nursing mothers or infants. Turmeric is “generally recognized as safe” (GRAS) as a food ingredient by the U.S. Food and Drug Administration. Turmeric is generally well tolerated even in high doses, but gastrointestinal side effects such as nausea and diarrhea, and rare allergic reactions have been reported, and it may increase the risk of bleeding in patients taking warfarin and antiplatelet drugs.
Because of a lack of data, turmeric in amounts higher than those found in foods as a flavoring should probably be avoided during breastfeeding.
Turmeric has been used as a galactogogue in India; however, no scientific data support this use. In Thailand it is reportedly used as part of a topical herbal mixture to shorten the time to full lactation and also part of a topical herbal mixture used for breast engorgement. Galactogogues should never replace evaluation and counseling on modifiable factors that affect milk production. In India turmeric is a component of a paste applied to the breasts for sore nipples. Contact dermatitis has been reported after contact of the skin with curcumin-containing products.
References from LactMed https://www.ncbi.nlm.nih.gov/books/NBK501846/
1.Sayed NZ, Deo R, Mukundan U. Herbal remedies used by Warlis of Dahanu to induce lactation in nursing mothers. Indian J Tradit Knowl. 2007;6:602-5.2.Chaudhuri RN, Ghosh BN, Chatterjee BN. Diet intake patterns of non-Bengali Muslim mothers during pregnancy and lactation. Indian J Public Health. 1989;33:82-3. [PubMed]3.Dhippayom T, Kongkaew C, Chaiyakunapruk N et al. Clinical effects of Thai herbal compress: A systematic review and meta-analysis. Evid Based Complement Alternat Med. 2015;2015:942378. [PMC free article] [PubMed]4.Ketsuwan S, Baiya N, Paritakul P et al. Effect of herbal compresses for maternal breast engorgement at postpartum: A randomized controlled trial. Breastfeed Med. 2018;13:361-5. [PubMed]5.Brodribb W. ABM Clinical Protocol #9: Use of galactogogues in initiating or augmenting maternal milk production, second revision 2018. Breastfeed Med. 2018;13:307-14. [PubMed]6.Amuthavalluvan V, Devarapalli J. Indigenous knowledge and health seeking behavior among Kattunayakan: a tribe in transition. Glob J Human Soc Sci. 2011;11. http://socialscienceresearch.org/index.php/GJHSS/article/view/198/161.7.Chaudhari SP, Tam AY, Barr JA. Curcumin: A contact allergen. J Clin Aesthet Dermatol. 2015;8:43-8. [PMC free article] [PubMed]